Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 70

$x=-4$

Since $\left(\frac{1}{5}\right)=5^{-1}$, then the equation becomes: \begin{align*}5^{x+3}=5^{-1}\end{align*} The base is the same on the 2 sides of the equation (and it is not 1), hence they will be equal if the exponents are equal. Thus, \begin{align*} x+3&=-1\\ x&=-1-3\\ x&=-4 \end{align*}