What happens if the panic level rises past 5?
Solution 1:
They cannot exceed five and wont. This is actually a 'tactic' in playing XCom. If you get any further missions this month, you should let the "5 panic" countries pass, since any extra panic will not be added.
Note: This does not apply to Terror missions; if you skip a "terror" mission the targeted country will leave the program right then and there.