Can I put a 3-gang box and a 2-gang box (Old Construction) just next to each other to make a 5-gang box?
If HD is your only option then they can order it for you. Here is one -

If you put two together then the spacing will not be right for the cover plate to line up for all switches.

They do make modular ones so you can daisy chain several together, I have seen them a lowes but i can not find a link. 

You may need to go to a dedicated electrical supply house.