Should I use tandem breakers or upgrade my panel?
Well first off - it really depends on what you are doing. Adding 5 Breakers sounds like a remodel operation and not a simple replace operation. 

Given that context - you need AFCI breakers to be up to code and AFCI breakers do not come in Tandem Breakers - you will need a new panel for that - look for one that has at least 40 Slots and more than 40 Circuits.