Answer: \(m = 5 \text{ or } m = -\frac{3}{5}\)
Product \(5\times(-15) = -75\), sum \(-22\): use \(-25\) and 3.
\[5m^2 - 22m - 15 = 0\]\[5m^2 - 25m + 3m - 15 = 0\]\[5m(m - 5) + 3(m - 5) = 0\]\[(m - 5)(5m + 3) = 0\]Equating each factor to zero gives the roots above.