The straightforward way to do this is to substitute the -2 for x and simplify:
Another way is to use synthetic division. (If you've never heard of synthetic division, then just simplify the expression above. Here's the synthetic division that tells us the value of the polynomial for x = -2:
-2 | -5 9 -3 -1
10 -38 82
-5 19 -41 81
The number in the lower right-hand corner, the 81, is the remainder when is divided by (x - (-2)). It is also the value of the polynomial when x = -2!!
This process involves no raising to a power. It can be a much easier way to evaluate polynomials, especially when the polynomial has large exponents.