Answer
$$
5^{x^{2}+x} =1
$$
The solution of the given equation is
$$
x=0 \text { or } \quad x=-1 .
$$
Work Step by Step
$$
5^{x^{2}+x} =1
$$
Since the bases must be the same, write 1 as $5^{0 }$ giving
$$
\begin{aligned} 5^{x^{2}+x} &=1 \\ 5^{x^{2}+x} &=5^{0} \\ x^{2}+x &=0 \\ x(x+1) &=0 \\ x=0 & \text { or } \quad x+1=0 \\ x=0 & \text { or } \quad x=-1 \end{aligned}
$$
So, the solution of the given equation is
$$
x=0 \text { or } \quad x=-1 .
$$
