If I buy a subscription for avast 4.8, will I need a new one when the next major release version 5 comes out?
Almost 100% no. I have a license until 2010 and the thought hadn’t even crossed my mind.
Apart from Alwil’s goodwill towards its customers, it’s standard industry practice to encourage migration to the safest/latest version.
No 
avast upgrade versions into the subscription period are allowed.