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Well, since we know the remainder is 5, We can see that x3+30x-c-5 when divided by x-5 leaves no remainder at all.
Given this, we can use knowledge to see that:
(x-5)(x2+5x+55) is equal to x3+30x-c-5.
We can multiply 55 and -5 to get -275, so c is 270.
-Random Person :)
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BTW THIS WAS AN EDIT, THE ANSWER FOR C is 270 NOT -270!!!