open G and A tuning

I apologize if this is a dumb question, but I’m a bit new to banjos (and string instruments in general). I saw that the strings included with the kits are recommended for open E tuning. I’ve been taking group classes with other banjos in open G tuning and fiddles in open A tuning.

I’m guessing that with E tuning, I could use my capo to tune up to G, but for A that would be five half steps which, I think, would not be possible to do with a capo due to the drone string starting on the fifth fret.

Would this be something I could fix by just tuning all the pegs a half step or two higher? Would I need to purchase different strings due to the increased tension? Would the neck and the rest of the hardware included with the kit be able to support that increased tension long term?