AMC 10 2021-fall-b Problem 23

Each of the $5{ }$ sides and the $5{ }$ diagonals of a regular pentagon are randomly and independently colored red or blue with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the pentagon such that all of its sides have the same color? $(\textbf{A})\: \frac23 (\textbf{B}) \: \frac{105}{128} (\textbf{C}) \: \frac{125}{128} (\textbf{D}) \: \frac{253}{256} (\textbf{E}) \: 1$