$\text { Write an equivalent series of the series } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { n } } { n ! } \text { with the index of summation }$

$\text { Write an equivalent series of the series } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { n } } { n ! } \text { with the index of summation }$ beginning at $n = 5$ .

A) $\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n - 5 } } { ( n - 5 ) ! }$
B) $\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n - 5 } } { n ! }$
C) $\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n + 5 } } { n ! }$
D) $\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n + 5 } } { ( n + 5 ) ! }$
E) $\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n } } { ( n - 5 ) ! }$