You can tune up the 5th string a step or so but after that you risk breaking it.
When you capo a banjo, you usually have 2 choices. You can install a 5th string capo which is a sliding capo that installs on the neck and capos only the 5th string.
You can install spikes, which are HO model railway spikes. These are hammered into the fretboard and used to hold down the 5th string, usually on frets 7, 8, 9 and 10. If you do this by yourself, do your research. The spikes have to placed in the right place and you have to drill the neck if you don’t want to split the fretboard.
A quick fix is to use the cap from a Bic pen. Cut the ‘clip’ end a bit and then jam it in between the 5th string and the fret.