The 7805 will not work with 4x 1.5V AA cells unless it is a low dropout version, it needs more than a 1v margin.
There are boost regs which increase source voltage, but I don't know of any that operate from 1.5v, usually about 2.5v is a minimum to get them going. That's why you don't find any digital electronics operating off a single 1.5v cell.
You can go with two batteries- 3v- and use a boost to get 5v, but that's unnecessarily complicated since you could probably just design your system to operate off of 3v. You'd need to check all your spec sheets for the ramifications of doing so, for one, you have to go with a lower clock freq.