Answer
$$1-5x+\sin(5x).$$
Work Step by Step
Since we have$$
1-\frac{5^{3} x^{3}}{3 !}+\frac{5^{5} x^{5}}{5 !}-\frac{5^{7} x^{7}}{7 !}+\cdots\\
= 1-\frac{(5x)^{3}}{3 !}+\frac{(5x)^{5}}{5 !}-\frac{(5x)^{7}}{7 !}+\cdots\\
=1-5x+5x-\frac{(5x)^{3}}{3 !}+\frac{(5x)^{5}}{5 !}-\frac{(5x)^{7}}{7 !}+\cdots
$$
Then by using Table 2, we see that this is a Maclaurin series of the function
$$1-5x+\sin(5x).$$
