Some cat 5e cables are able to do up to 10gbps for short distances (less than 30 meters).

2.5gbps and even 5gbps should be achievable for most cat 5e cables.

Your cat 5 cables could be a bottleneck depending on their quality. If they are high quality they should be able to achieve 1gbps over short distances (30-35 meters).

However your router only has 1gbps so it doesn’t make sense to upgrade your cables unless you also upgrade your router (and presumably your network cards).

If you decide to upgrade your networking I’d recommend that you buy cat 6a cables.

Cat 7 is only a standard recognized by ISO if I’m not mistaken so finding good cables is harder.

And cat 8 is the newest standard recognized by both ISO and IEEE, but it’s too expensive for home users.