The longest known cycle length of generalized collatz $5x+1$ trajectory

Question

The generalized collatz $5x+1$ trajectory, if $n$ is even then divide $n$ by $2$, and if $n$ odd then multiply $n$ by $5$ and then add $1$. For example if $n=3$, we have $3=>16=>8=>4=>2=>1=>6=>3$, so the cycle length is $7$. If n=$5$, we have $$5=>26=>13=>66=>33=>166=>83=>416=>208=>104=>52=>26=>13$$ So the cycle length is $10$. I've checked n up to $100$ and many of the trajectories seemed to be"escape to infinity". Does anyone know the other cycle length other than $7$ and $10$ $?$