The answer is $32$.
Its supposed to be $2^5$ but I do not see how you get that?
The way I see it, there are $5$ ways to go up and $5$ ways to go right, total ways = $5x5= 25$
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Each time you have to choose where to go, you have 2 options: up or right. Now observe that no matter how you get to the diagonal, you will have made 5 choices. So you have to choose between 2 options 5 times, which gives us $$2\cdot2\cdot2\cdot2\cdot2 = 2^5$$ possible choices.