Cat5e is is certified to a higher specification. Higher frequencies, better crosstalk margins, etc.
Gig runs on Cat5 OK, but 5e or 6 is preferred/recommended because it is certified to a higher spec.
Make sure all of your components (plugs, jacks, panels, jumpers, in-wall cabling) are rated at the same level. The end-to-end system takes on the rating of the lowest-rated component in the chain.
FWIW
Scott