What are the solutions of the inequality (x-3) (x+5) <=0

Assuming that the inequality you were going for was a ≤, set both polynomials less than or equal to 0.

x - 3 ≤ 0

x + 5 ≤ 0

For the first equation add 3 to both sides of the inequality. For the second, subtract 5 from both sides.

x ≤ 3

x ≤ - 5

These would be your solutions I guess, however, if you want to expand upon that, your actual answer is ( - ∞, - 5] because if you were to plot these two inequalities on a number line, that is where the overlap would occur.