State whether it is a pure surd or mixed surd $5\sqrt{7}$

The correct option is D Mixed surd
A surd having a rational co-efficient other than unity is called a mixed surd.
In other words if some part of the quantity under the radical sign is taken out of it, then it makes the mixed surd
Thus, $5\sqrt{7}$ is a mixed surd as $5$ is outside the radical sign and $\sqrt{7}$ is a surd