2024 Mock AMC 10 - Problem 8

Shiro has 26 unique blocks arranged in a circle and wants to paint 5. He starts by choosing any starting block to paint. Each subsequent painted block must be separated from the previous one by no more than 4 blocks, and a block can only be painted once. How many distinct combinations of blocks can Shiro paint? Two combinations are considered different if they differ in at least one painted block, regardless of the order in which they were painted.

\textbf{(A) }16250\qquad\textbf{(B) }2600000\qquad\textbf{(C) }100000\qquad\textbf{(D) }11881376\qquad\textbf{(E) }260000