In reality, very little. Category 5e was established to allow Gigabit Ethernet while category 5 is limited to 100BaseT, even though it was envisioned to run 1000BaseT before the standard was fully established. It's just a little tighter spec that takes into account Return Loss as well Power Sum properties of the cable system.
Category 5 standards have been deleted in the standards and are now a footnote. If you have a category 5 plant you could attempt to test it to category 5e standards using a Type II or better tester, about 75% of the old category 5 plants do pass category 5e testing standards in my experience.
Joseph Golan, RCDD