A change from Cartesian to polar coordinates involves the following transformation: $x = r \cos \theta$ and $y = r \sin \theta$. For a circle with polar equation $r = \binom{m}{n} \cos \theta$, where $1 \leq n \leq m \leq 6$, how many distinct combinations of $m$ and $n$ will this equation represent a circle of radius greater than or equal to $5$?