Express $\frac{6!+4!}{5!}$ as a mixed number.
We can separate the fraction to get $\frac{6!}{5!} +\frac{4!}{5!}$. We can then simplify the quotient of factorials:

\begin{align*}
\frac{6!}{5!} +\frac{4!}{5!} &= \frac{6\cdot5!}{5!} +\frac{4!}{5\cdot4!}\\
&=6+\frac15\\
&=\boxed{6\frac15}.
\end{align*}