We first simplify the expression by multiplying the two terms in the brackets:

(x^15 + 5)(x^3 + 2) = x^18 + 2x^15 + 5x^3 + 10

Now, we subtract (10 + x^18) from the above expression:

(x^18 + 2x^15 + 5x^3 + 10) - (10 + x^18)
= x^18 + 2x^15 + 5x^3 + 10 - 10 - x^18
= 2x^15 + 5x^3

Therefore, the simplified expression is 2x^15 + 5x^3.