Cat5 cables were the best option for wired networking (also called Ethernet) for a long time. But since the release of Cat6, that's changed. Cat6 is now considered the minimum standard for networking, ...
Cat6 and faster cables are overkill for most people.
If you are cabling for 1000BT, you want CAT5e at a minimum. CAT 5 does not do gigabit as part of the spec. CAT6 just gives you more bandwidth, but there are no Ethernet standards that require it yet.
If you've been facing slow internet and lagging issues despite paying for a premium internet plan, the advice you've probably gotten from most people is to switch to using Ethernet. Following this ...