y = 5x – 7 has slope which is the coefficient of x or 5.

A line perpendicular to that line would have a slope which
is its negative reciprocal or -1/5, so that narrows the 
correct choice down to either y = –1/5x – 7 or y = –1/5x + 1.

So we need only to find out which one is satisfied by (-10,3).
Substituting x=-10 and y = 3 in

y = –1/5x – 7
3 = -1/5(-10) - 7
3 = 2-7
3 = -5
That's false, so that's not it.

So it can only be 

y = –1/5x + 1.   Check to make sure:
3 = -1/5(-10) + 1
3 = 2+1
3 = 3

That's true.  So the answer is y = –1/5x + 1

Edwin