#### Answer

A: $(5,0,10)$
B: $(0,8,0)$
C: $(5,8,10)$

#### Work Step by Step

Given the two vertices, we find the maximum value for each coordinate is $x=5$, $y=8$, and $z=10$.
A is on the $xz$-plane, so the $y$ coordinate is zero. Thus, A is at $(5,0,10)$.
B is on the $yz$-plane and $xy$-plane, so the $x$ and $z$ coordinate is zero. Thus, B is at $(0,8,0)$.
C is directly on top of the vertex $(5,8,0)$, meaning that only the $z$ coordinate is different. C is on the same plane as $(0,0,10)$, making the $z$ coordinate $10$. Thus, C is at $(5,8,10)$.