Can you buy crypto, and sell it 5 minutes or so later?
Yes you can do that, when you are trading at exchanges what you trader there will be instantly credited to your account,but i dont think that you will gain profit from reselling it after 5 mins.
You should not do this plan when trading it wont benefit you at all and you may take a large loss from doing this kind of strategy.
Is there a problem with the time it takes to show in your wallet after buying?
No there is no time delay when buying or trading at exchanges, but there will be some delays when the wallet of an exchange like yobit is on maintenance.