Since we're given two quadratic equations \(\displaystyle a^2=3a+5\) and \(\displaystyle b^2=3b+5\) and that \(\displaystyle a\ne b\), we can tell by quadratic formula that
\(\displaystyle a=\frac{3+ \sqrt{29}}{2}\) and \(\displaystyle b=\frac{3- \sqrt{29}}{2}\).
Thus, \(\displaystyle a+b=3\) and \(\displaystyle ab=-5\).