Cables don't get "old" by themselves, but they might have been installed incorrectly from the start (too tight bending, swapped pairs/cables, twisted pairs separated for a longer distance, shields not connected properly, grounding done wrong). Furthermore mechanical stress (too much work being done on a patch panel over the course of several years, cables pulled hard while moving racks, ...) might have damaged parts of the cabling.
To cut a long story short: Properly done CAT5 should be good enough for Gigabit, but often what's called CAT5 works well for 100 Mbit networks even though it doesn't meet the specs.
Get a decent LAN tester (not just two computers, using "ping") that prints out attenuation, crosstalk and all the other things... and preferably tells you what "category" your cabling still is compatible with. Replace all the stuff that's out of spec. Then you have hard numbers you can rely on should you ever ponder if your local network infrastructure can handle 100M/1G/10G bit/s. Everything else is guesswork.