jmc

Taking the conjugate of both sides, we get $$\overline{a\overline{b}}=\overline{-1+5i}=-1-5i.$$But $\overline{a\overline{b}}=\overline{a}\overline{\overline{b}}=\overline{a}b,$ so $$\overline{a}b=\boxed{-1-5i}.$$