Deck plans - joist and beam sizing
First of all your statement re 5-6 feet on center makes no sense. Your local code want you to go down to virgin soil, and that is probably why you have to go that deep if you are 5-6 feet of your foundation.
You dont say what kind of live load you are planning on putting on your deck, so how can anyone say what you need?
Ledger strip? I through bolted a 2 x 10 plate to my rim joist with 5/8 HD Galvanized Bolts with large flat washers inside and out, 16 inches on center. I used Simpson hangers and 2 x 10 joists 16 inches on center to span 12 feet with a two foot cantilever over a triple 2 x 12. Mine was rated at 100 lb live load.
You have to do the math, my friend.
" A lot of men build things, and a lot of things fall down "