smc

Without loss of generality, let $A$ be on the $x$ axis, $B$ be on the $y$ axis, and $C$ be on the $z$ axis, and let $AB,BC,CA$ have respective lengths of 5, 6, and 7. Let $a,b,c$ denote the lengths of segments $OA,OB,OC,$ respectively. Then by the Pythagorean Theorem, $$\begin{array}{rl}{a}^2+b^2& =5^2,\\ b^2+c^2& =6^2,\\ c^2+a^2& =7^2,\end{array}$$ so $a^2=(5^2+7^2-6^2)/2=19$; similarly, $b^2=6$ and $c^2=30$. Since $OA$, $OB$, and $OC$ are mutually perpendicular, the tetrahedron's volume is $$abc/6$$ because we can consider the tetrahedron to be a right triangular pyramid. $$abc/6=\sqrt{a^2{b}^2{c}^2}/6=\frac{\sqrt{19\cdot 6\cdot 30}}{6}=\sqrt{95},$$ which is answer choice $\boxed{\sqrt{95}}$.