I just made my first DIY speaker cables. I used CAT5 and terminated with banana plugs. The question is, at the tip of cable where copper is exposed, will get oxidized over period time even if it is inserted into banana plugs? Is there away to prevent copper to be oxidized?

Tin the ends of the wires.

If it's crimped,soldered, or just generally terminated properly, there will not be any corrosion.

I use Noalox anti-oxidant joint compound. It is intended for use in aluminum to aluminum/copper connections. It is a medium gray toothpaste-type material.

I have used it successfully for 30 years in ham radio. Outdoors, any electrical connection gets coated with the stuff. Round aluminum tubing that slides inside progressively smaller pieces gets coated. Years later, no corrosion and the tubing looks brand new. It is not affected by sun or water.

Indoors, I even coat the threads on light bulbs. If they burn out, they easily screw out for replacement. Wires twisted and capped get coated internally.

Solder is good but with movement it can crack and oxidation gets in the crack and things become intermittent.

It's great stuff.
Take Aim, W4MAN