all pairs of spins have probabilty of \(\left(\dfrac 1 5\right)^2 = \dfrac{1}{25}\)
so we just have to count the number of spin pairs where Jane wins and divide it by 25.
there's no magic to this, just list them out. If I understand what "non-negative difference" means, Jane wins with
(5,5), (5,4), (5,3), (4,5), (4,4), (4,3), (4,2), (3,5), (3,4), (3,3), (3,2), (3,1), (2,4), (2,3), (2,2), (2,1), (1,3), (1,2), (1,1)
i.e. 19 spin combos that lead to Jane winning. Thus
\(P[\text{Jane wins}]=\dfrac{19}{25}\)
.