Step 1 :Expand the expression: \((x - 3)(5x + 2) = 5x^2 - 15x + 2x - 6\)
Step 2 :Combine like terms: \(5x^2 - 15x + 2x - 6 = 5x^2 - 13x - 6\)
Step 3 :\(\boxed{5x^2 - 13x - 6}\)