A fair die is rolled 5 times resulting in outcomes $X_i$, with $i=1,\dots,5$. Find $P(X_2+X_3<X_3+X_4)$

I was looking at the solutions to this problem:

A fair die is rolled 5 times resulting in outcomes $X_i$, with $i=1,\dots,5$.

Find $P(X_2+X_3<X_3+X_4)$.

Why does that probability equate to $P(X_3<X_4)$? Shouldn't it be $P(X_2<X_4)$?

Note that if $i\not=j$ then $P(X_i<X_j)$ are all equal to $$\frac{5+4+3+2+1}{36} =\frac{15}{36}=\frac{5}{12},$$ or $$\frac{1-\frac{6}{36}}{2}=\frac{15}{36}=\frac{5}{12}.$$