2013 Pascal Problem 10

The time on a cell phone is 3{:}52. How many minutes will pass before the phone next shows a time using each of the digits 2, 3 and 5 exactly once?

\textbf{(A)}\ 27\quad \textbf{(B)}\ 59\quad \textbf{(C)}\ 77\quad \textbf{(D)}\ 91\quad \textbf{(E)}\ 171

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.