1. The problem is to find a quadratic equation with integer coefficients given the solutions $x = -5$ and $x = 3$. 2. The formula for a quadratic equation with roots $r_1$ and $r_2$ is: $$ (x - r_1)(x - r_2) = 0 $$ 3. Substitute the given roots: $$ (x - (-5))(x - 3) = (x + 5)(x - 3) = 0 $$ 4. Expand the product: $$ x^2 - 3x + 5x - 15 = x^2 + 2x - 15 $$ 5. Therefore, the quadratic equation with integer coefficients is: $$ x^2 + 2x - 15 = 0 $$ This equation has the given solutions $x = -5$ and $x = 3$ as required.