From a combination of archaeology, linguistic analysis, and sheer guesswork, we can put the period when they lived, at 5000 - 3000 BCE. We can't be more accurate than that for several reasons. First, the data won't allow us to be. There is enough slippage in each variable that taken as a whole we cannot be precise. Second, there are questions of definition. From what I said above, it might have seemed as if "Proto-Indo-European" referred to a slice in time. But languages and cultures grow and change and wither. What is the language called "English?" Is it Old English? Middle English? Modern English? And what period within each of these? Is it the Modern English of Shakespeare, or of TV broadcasters? In the same way, PIE existed over a long period of time, and it is wrong to point to one exact period and say: this is PIE. Finally, there is the question of dialects. Just as British English and American English differ in vocabulary, grammar, and pronunciation, so too were there dialects of PIE. Some may have differed because of space, and some because of time.
This may seem like waffling. Get used to it; what seems like waffling is pretty standard when dealing with a subject like this.
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