Triangle from a fixed loaf and a randomly cut one

You have two bread loaves of lengths $5$ and $8$. The length-$8$ loaf is cut once at a point chosen uniformly along it. What is the probability that the length-$5$ loaf together with the two pieces can serve as the sides of a triangle?

$5/8$. With cut point $X\sim\text{Unif}(0,8)$ the sides are $5$, $X$, $8-X$. The triangle inequalities reduce to $X<6.5$ and $X>1.5$, an interval of length $5$ out of $8$.