If you have 5" remaining, you have slightly less than a 2x6 in strength, so
you can look that up in the spanning tables. What are you planning on using
for the treads? You almost certainly need a third stringer just from that
perspective. When I built our deck, I actually used four stringers, because
the minimum spanning distance on stairs for the composite decking I was
using for the treads was only 12". I then put some X-bracing underneath the
four treads and they are rock solid -- not even a hint of bounce on them.

Don't skimp on this, it won't cost much more in the grand scheme of things
and you'll be happier if the deck and stairway doesn't bounce (our old deck
swayed if you leaned up against the railing and wiggled-- our new
replacement, which is quite a bit bigger, won't budge).

-Tim