Think about powers of $5$: $5^2=25$. What do you get if you multiply by $5$ one more time? How can you write $125$ as $5^{\text{something}}$?

Once both sides are written as powers of $5$, what must be true about their exponents if the two expressions are equal?

In Desmos, enter the function y = 5^(x-1) to graph $h(x)$.

On a new line, enter y = 125 to draw a horizontal line representing where $h(x)=125$.

Click on the point where the graph of y = 5^(x-1) intersects the line y = 125. The x-coordinate of this intersection is the value of $x$ that solves the equation.

You are told that $h(x)=5^{x-1}$ and asked for the value of $x$ when $h(x)=125$.

So you need to solve the equation

$5^{x-1}=125$.

Notice that $125$ is a power of $5$:

$5\cdot 5=25$ and $25\cdot 5=125$, so $125=5^3$.

Substitute this into the equation:

$5^{x-1}=5^3$.

When two powers with the same base are equal, their exponents must be equal. So from

you get

Add $1$ to both sides:

So the value of $x$ that makes $h(x)=125$ is $4$.