Answer
These quantum numbers are possible.
Work Step by Step
For each $n$, the values of $l$ can be $~~l = 0, 1, 2,...,(n-1)$
For each $l,$ the values of $m_l$ can be $~~m_l = 0, \pm 1, \pm 2,...,\pm l$
In this case: $~~n = 5, ~~l=3, ~~m_l = -2$
These quantum numbers are possible.
