A triangular number is a positive integer that can be expressed in the form $t_n=1+2+3+\cdots +n$, for some positive integer $n$. The three smallest triangular numbers that are also perfect squares are $t_1=1=1^2$, $t_8=36=6^2$, and $t_{49}=1225=35^2$. What is the value of $n$ for the fifth smallest triangular number that is also a perfect square?