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What's that saying? If you have to ask then you already know the answer. App o Rama or App Spree has nothing to do with why you are doing it. Its purely about numbers and you are well over it. Personally, I consider anything more than 2 an app spree.
New cards or applications affect your FICO score in a few ways.
1) Any new account will drop your score temporarily (say about 6 months).
2) Inquiries will affect your score for up to 2 years with the effect dropping every month. If all 5 inquiries goes on an inquiry free credit report, I would guess a 40-50 point hit initially. Funny thing is that 10 inquiries would probably only be like 50-55.
3) AAoA drop: Adding new accounts will drop your Average Age of Accounts. FICO uses this to score. No way to know how much effect it will have on your credit report as you gave us no details on your credit file.
4) Reduced Utilization: Your utilization percentage should go down and therefore raise your score unless you are already sub 10%.
Given these 4 factors, you should be able to answer your own question as to how long your FICO will be affected for. As for score drop, unless you give a lot more details, no one can even guess for you.