~~~~

Well, since we know the remainder is 5, We can see that x^{3}+30x-c-5 when divided by x-5 leaves no remainder at all.

Given this, we can use knowledge to see that:

(x-5)(x^{2}+5x+55) is equal to x^{3}+30x-c-5.

We can multiply 55 and -5 to get -275, so c is 270.

-Random Person :)

~~~~

BTW THIS WAS AN EDIT, THE ANSWER FOR C is 270 NOT -270!!!