History conventionally begins with the development of writing, which was around 5,200 years ago, so if you're looking for written material that can be used to guess at dates, then yes, that's how far back we can date stuff.

Ancient Egyptian dates are among the oldest, and they go back around that far (~5,200) years. They are relative, dating events like "in the 5th year of the reign of Pharaoh Whatshisname", so you then have to find out when Pharaoh Whathisname began his rule. We have estimates, but you usually can't pin stuff down to the exact year, as the chronology continues to be revised constantly.

So if by "ability to date" you mean "assign a date based on some formula based on historic events", then yes, that's probably about as far as we can go. You can find an inscription saying something happened in the n'th year of king z, and you can look up your chronology and calculate and say "that corresponds to the year 2213 BC in our modern dating". Whether it really happened in 2213 BC or not is anyone's guess, because the hook such dates are hung on (king z's reign) are themselves not that certain and frequently revised. But yes, you're somewhere in the ballpark with such dates.

Of course, we can date much older objects with different radionuclide dating methods. For example, radiocarbon dating works well up to about 50,000 years, and in extreme cases up to 75,000 years. It has its own error margins. Even with perfect samples and faultless technique, there are systemic uncertainties that can't be avoided. So radiocarbon dates are reported with the error estimates, like "4627 plus or minus 80 years". The error bars grow larger the older the sample, so a 50,000 year old date may have error bars of 500 years on each side.

Other radiometric methods can date much older material. Uranium-Lead dating works over the 1 million to 4.5 billion year range (as old as the Earth itself), with best case errors of around 0.1%. Potassium-Argon works from about 100,000 years to 4.5 billion years. There are half a dozen other similar dating techniques. But I presume you're not interested in these since they're not dating anything related to human history.

We can certainly find old artifacts made by humans and use physical techniques such as radiometry to produce dates far older than 5,200 years. All the Venus figurines, the ancient cave paintings, bone flutes, spearheads and axes, old tools - have all been dated by physical methods to dates as old as 125,000 years.