So, I love the premise of the question, but within the parameters you've given we run into a problem. You've cleverly picked time periods before and after "classical" Latin (the Latin of the ancient Romans as opposed to its use during the Middle Ages as a sort of ecclesiastical/elite second language, to simplify things) with the core of classical Latin literature coming from around the 1st century BC/AD. Your end date of 400 gives us a good bookend to a Latin-speaking Roman political entity -- Latin would continue to be spoken by Romans as the western empire is conquered by different Germanic groups, and even adopted by these new elites, but by 600 the divergence into the early Romance languages is pretty complete and we generally stop calling the language Latin. There are some significant changes by this point, such that a separate university course on Late Latin is often offered to acclimatize classical readers to it, but this has a great deal to do with a change in the audience, as (to grossly oversimplify things) cultural changes including the growth of Christianity have led to the prevalence of the Latin spoken by lower classes ("Vulgar" Latin) appearing alongside/in place of the Latin of the elites in literature. In any case, a classical Latin scholar will have very little difficulty in reading Jerome's Vulgate Bible, as an example of a text from the period. I find the 2nd chapter of Luke to be a handy Christmas-time text teaching Latin at a (religious) high school; only a few notes on vocabulary are necessary.

At the core of the problem, though, the Latin of 500 BC is a very different animal, primarily because we just have incredibly little -- a few fragmentary inscriptions that are often too short to get much of a handle on, but there is enough to say it's got very significant differences. I challenge a casual reader of Classical Latin to attempt to make anything out of the text of the Lapis Niger:

I a 1 quoiho... b 2-3 sakros: es/ed:sord... II a 4-5 ...iaias/recei: lo... b 6-7 ...euam/quos: re... III a 8-9 ...m: kalato/rem: ha.... b 10-11 ...od: io: uxmen/takapia: dotau... IV a 12 ...m: i: te: r p e b 13-14 ...m: quoiha/uelod: nequ... c 15 ...od: iouestod/ V 16 loiuquiodpo

It's difficult to quantify mutual intelligibility, but there are far greater qualitative differences between 500 BC and 1 AD than there are between 1 AD and 400 AD. Even in a significantly closer timescale to the classics, it is quite punishing for a modern reader who's quite fluent in Classical Latin to get a hang of Roman Comedy from just the third and second centuries BC, although they were certainly still intelligible to classical audiences as they were still performed. It might be useful but unscientific to consider the way that Shakespeare is perhaps difficult but understandable to us. Classical Romans also seem to have been occasionally mystified by the archaic Latin of their own religious rites, repeating phrases because they are required by ritual instead of understanding what they meant.

In the absence, again, of a good scientific method for measuring intelligibility of a language between two third parties, then, I'd posit that, qualitatively by having students familiar with classical attempt to read texts from other time periods, the difference between 1st and 4th century AD Latin gives no real problem to mutual understanding, nor a significant one between 3rd and 1st BC, but the Latin of 500 BC is a hard question to answer; still, I suspect they would be much more difficult to understand for the other time periods.

Adding on a bit of further reading: Harrington's Medieval Latin is, so far as I know, the go-to text for getting into late Latin for students already familiar with classical. The emphasis is mostly on well after your time period, but Part One does explore Late Antique Latin, and in addition to the Jerome I mentioned above, it reminds me that Egeria (the journal of a nun traveling to the Holy Land) is an excellent snapshot of Latin from near 400 AD. Grangent from the early 20th century wrote a pretty standard introduction to the mechanics of Vulgate Latin. There's less good reading on the Latin of the Roman comedies other than the texts themselves, but the standard book to point you to there is Bennett's Syntax of Early Latin. These books will unfortunately be much more useful if you're already familiar with Classical Latin (for which there are scads of texts) to have a basis for comparison.

Hey there,

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All of these comments get removed on /r/AskHistorians because the huge majority of our subscribers really do want accurate, comprehensive, in-depth historical answers based on good historical practice and high-quality sources. It's amazing how many downvotes and reports an obvious shitpost can attract on a popular thread on /r/AskHistorians within minutes, thanks to our readers (if you see it, report it!)

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Edit: in the three hours it took me to write this (on and off) u/QVCatullus wrote an excellent response. Make sure you read it!

The short answer: Our 500 BC Roman is going to struggle in 400 AD. In the reverse situation, our 400 AD Roman may fair better, depending on their level of education.

The long answer: We have two complicating factors here, the first being the temporal change in Latin between our two Romans, and the second being the social/functional varieties of Latin in use in 400 AD.

Our 500 BC Roman is speaking Prisca Latinitas, the variety of Latin dating to at least the Early Republic period, and so named by Romans in the 'Classical Era' such as Cicero and Tacitus, in reference to the viri prisci, the very earliest Romans. Cicero in particular, in De Oratore, mentions how elements of this old style of latin are maintained in turns of phrase still used by him and his contemporaries, but refers to them as "verborum vetustas prisca" or words with archaic characteristics.

While we don't have a wealth of inscriptions from this period, some do exist with some certainty of date, and show a pronounced difference from later Latin texts. If we are looking at the 500 BC, inscriptions from this period still use the Etruscan alphabet, or in the case of the Lapis Niger inscription from the forum at Rome, a hybridized Greek style lettering. While the visual differences are striking, as far as I'm aware there is no way determine the spoken peculiarities of Latin from this period. By the 3rd C, Prisca Latintas appears in literary works using the familiar latin alphabet. There are still marked differences in these texts that would have impacted pronunciation.

By the beginning of the Roman Empire, Latin has taken on two forms: Classical and common. Classical Latin as we know it was the result of standardization through prescriptive language education. In its spoken form, it was called Sermo Latinus. It was rigid and long lasting. and while it may have preserved some of those archaic phrases mentioned by Cicero, there is a very specific problem facing the 500 BC Roman, and that is the common form. While Sermo Latinus was used for all things official, a type of 'slang' latin, or Sermo Vulgaris, developed to be used by common folks in day to day dealings. Sermo Latinus in the streets, Sermo Vulgaris in the sheets, if you will.

While the formal type of Latin had a strict orthography, the slang variety (perhaps obviously) did not. So over time, the divide between formal written works in Latin and day to day speech in Latin grew. This is how we arrived at our romance languages, through the gradual regionalized changes to common Latin (although I am Not qualified to speak to that process).

Now to the point - provided our 500 BC Roman arrived in 400 AD in the city of Rome itself, and not other parts of the Roman world which would have their own language peculiarities, he would likely be speaking with someone using a form of slang latin developed over centuries. Sure, nouns and verbs would share phonetic roots that each would likely feel were familiar, but enough grammatical changes would have emerged to make communication difficult.

Caveat - I work occasionally with Roman inscription, but I only have my undergraduate experience with Roman literature, early or otherwise. So I have tried to cobble this together out of concepts I am familiar with. I am hoping this can be the starting point of a discussion that helps answer OP's question. With any luck, a Latin Philologist will come along and tear apart my inaccuracies. Also this had to get written piecemeal over the course of my morning, so I apologize about the writing quality.