This is not a Binary Operation and you would have to be a masochist to use FOIL to solve it... I'm guessing that's because you typed it in wrong and the exponent wirtten as "5" should be "2". (I'm also guessing that just maybe you mean binomial operations, rather than binary operations. The vast vast majority of 'pre-pre-calculus' taught as math in school is binary operations...)

If that is the case, then things aren't so tough. Consider the (2x^2-6)^2 term by itself for a sec, it can also be written (2x^2-6)*(2x^2-6). With foil:

F (first terms): 2x^2 * 2x^2 = 4x^4
O (outside terms): 2x^2 * -6 = -12x^2
I (inside terms): -6 * 2x^2 = -12x^2
L (last terms): -6 * -6 = 36

The sum of these terms is:
4x^4 - 24x^2 + 36
Multiplied by five gives:
20x^2 - 100x^2 + 180
Added to 6x+7:
20x^4 -100x^2 + 6x + 187

(If you did type it right, then the answer is, if my multiplication doesn't suck, 160x^10 - 2400x^8 + 14400x^6 - 43200x^4 + 64800x^2 + 6x - 38873... which isn't a polynomial I'd soon force on a student still dealing with FOIL)

A note to the others in this thread; the term 'binary operation' tends more two refer to operations with arity two (addition and multiplication being prime examples) rather than operations involving the Binomial Number System.