\(log_5\frac{4\sqrt{2}}{\sqrt{15}}=log_5\left(4\sqrt{2}\right)-log_5\left(\sqrt{15}\right)\)
\(=log_5\left(2^{\frac{5}{2}}\right)-log_5\left(\sqrt{3}\right)-log_5\left(\sqrt{5}\right)\)
\(=\frac{5}{2}log_52-\frac{1}{2}log_53-\frac{1}{2}\)
\(=\frac{5a-b-1}{2}\)