Why won’t my gear change off of 5? My bike is a pretty terrible mountain bike held together by duct tape and I just fixed an issue with the brakes rubbing on the wheel slowing it down. And now my gears stop working. No matter what I change the gear shift to, the chain stays on the 5th gear (second smallest). I was cycling the other day and manually moved the chain onto the 4th gear, and even though my shift was on 4, it moved itself back to 5. Any idea how to fix this? Cycling on only gear 5 is very tiring.
More information would be helpful such as type of shifter, derailleur etc, but first of all look at the derailleur and either shift or have someone shift to a different gear (can be done while parked). If there is no movement on the derailleur you likely have a cable that has either A) come loose from its connection B) Broken or C)stretched over time and become so loose that it is not shifting. 

It sounds like the shifter is doing nothing at all which makes me think the cable is either not connected (at the shifter or derailleur) or too loose, it could also be that the internal mechanism of the shifter is broken if you find that the cable is still tight, but that is the first thing i would check.

I have also had a cable pull out of the cable clamp at the derailleur which had apparently loosened up over time and when shifted the cable would just slide back and forth through that connection. Easily fixed by pulling the cable back tight and retightening the clamp.

If the bike is up there in age, you may look into replacing all the cables and making sure everything is properly lubricated as well. This is relatively easy to do yourself with some YouTube videos and google. 

Sidenote, hopefully it is not truly duck tape that is holding the bike together.. sounds dangerous :)