So I've had this doubt for a while now and haven't been able to find much on this subject. As we can see from English for example, languages tend to evolve over time and for many people it is quite difficult to understand someone speaking Middle or Old English. A modern English speaker would have some trouble conversing with someone from the 1100s for example.
Since the Roman republic and later the Empire were so long lived, there had to have been some changes and evolution in the language commonly spoken. So do we have any information on how Latin evolved both in writing and pronunciation and would a Roman from the 5th century BC be able to understand and talk to a Roman from the 5th century AD? Would they be able to easily read and understand documents from the early republic as well?
There is a lot of scholarship about Roman pronunciation, but I don't know very much about it, so I'll leave that element to someone else. In terms of writing and grammar, they are noticeably different but mutually intelligible. They have different conventions for how sentences look, and different words were popular at different times, but they're easily recognizable as the same language. I would say it's roughly analogous to how a contemporary American English speaker might have trouble understanding Shakespeare's English at first, but once they learn the most common words he uses and get used to the sentence structure, it's not that hard.