Brilli the Ant is Brilliant!

Brilli the ant sits on the Cartesian Plane at (0,0). It takes him 1 minute to crawl 1 unit. Brilli only moves horizontally and vertically. The probability that after 5 minutes he is on (2,3) is \( \frac{m}{n} \) where m and n are realitively prime. What is \( \frac{m+n}{2} \) to the nearest whole number?

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