Evaluate the Iterated Integral by Converting to Polar Coordinates $$\int _ { - 5 } ^ { 5 } \int _ { 0 } ^ { \sqrt { 25 - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } d x d y .$$

Multiple Choice

Evaluate the iterated integral by converting to polar coordinates. Round the answer to two decimal places.
$$\int _ { - 5 } ^ { 5 } \int _ { 0 } ^ { \sqrt { 25 - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } d x d y .$$

A) $1963.5$
B) $15.71$
C) $4908.74$
D) $39.27$
E) 625