Identify the most simplified version of the expression below: \[ \sqrt{5}+4 \sqrt{45} \] \( \begin{array}{ll}\text { A) } 4 \sqrt{50} & \text { C) } 13 \sqrt{5} \\ \text { B) } 20 \sqrt{2} & \text { D) } 37 \sqrt{5}\end{array} \)

To simplify the expression \(\sqrt{5}+4 \sqrt{45}\), start by simplifying \(\sqrt{45}\): \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \] Now substitute this back into the expression: \[ 4\sqrt{45} = 4 \cdot 3\sqrt{5} = 12\sqrt{5} \] Now, add this to \(\sqrt{5}\): \[ \sqrt{5} + 12\sqrt{5} = (1 + 12)\sqrt{5} = 13\sqrt{5} \] Thus, the most simplified version of the expression is: \[ \boxed{13\sqrt{5}} \] So the correct answer is option C) 13 \(\sqrt{5}\).