Well built quality guns can have tens of thousands of rounds through them and still be worthwhile. Inexpensive pocket guns might be worn out in a couple thousand.
I have about 10-12k rounds through a browning buckmark and I still consider it new. I have 6-7k through a Glock 29 and consider it nicely broken in. I put 5-6k through a Taurus .357 and figured it was about a third of the way through its life.
I would be more interested in looking the gun over.
1. A properly cared for gun with 5k rounds could be in better condition than one that only has 2k through it. Recoil springs and other parts that require changing can have a big impact on wear over the life of the gun.
2. The owner may not actually know/be lying about the count.
If buying a used gun I would buy one that has a lifetime warranty that sticks to the gun not just the first owner, like a taurus does, that way it doesnt matter how many rounds are through it, if it ever breaks they fix it free of charge everytime, and if it cant be fixed they'll REPLACE IT FREE, thats the way to go in my opinion
You cabn dang near use used car Criteria for a used gun. Is the finnish badly worn (old dull Paint), does it look like the seller is trying to cover something up, Bluing looks funny (like Bondo over rust on a car), fit ,loose or tight excess wear on parts,(Fit of hood,doors glass, ect on a car). Is it dirty or generally looks like it wasn't cared for. You get the idea!
It all depends on the gun, and more so, the previous owner. In my opinion, most modern firearms are capable of thousands. Some are more apt to have problems, but most well-known gun makes and models made within the last 10 years or so are designed to take probably more rounds than most people could put through them. This is true of course, if the weapon has been well cared for.
depends on the gun. i have two glocks i bought used that i have no idea how many rounds were through them. i have never had a single problem out of either of them. just give it a good inspection and you should be alright. if you dont quite know what to look for in a used gun then take a friend with you that could help look at it. i would be more worried about do it yourself mods like trigger job or messing with the feedramp than round count. good luck