#### Answer

It can be seen that Mark incorrectly simplified the square root of 10 to 5.
The correct answer is $xy^{4}\sqrt {10}$.

#### Work Step by Step

Step 1: We will solve the expression to find the correct answer and to determine Mark's mistake.
Step 2: $\sqrt {10x^{2}y^{8}}$
Step 3: $\sqrt {10}\times\sqrt {x^{2}}\times\sqrt {y^{8}}$
Step 4: $\sqrt {10}\times(x)^{2\times\frac{1}{2}}\times (y)^{8\times\frac{1}{2}}$
Step 5: $\sqrt {10}\times(x)\times (y)^{4}$
Step 6: Therefore, the correct answer is $xy^{4}\sqrt {10}$.
Step 7: It can be seen that Mark incorrectly simplified the square root of 10 to 5.