We can find the units digit of $5^4$ by finding the units digit of $5$, $5^2$, $5^3$, and $5^4$.
The units digit of $5$ is $5$.
The units digit of $5^2$ is the units digit of $5 \times 5$, which is $25$, so the units digit is $5$.
The units digit of $5^3$ is the units digit of $5 \times 5 \times 5$, which is $125$, so the units digit is $5$.
The units digit of $5^4$ is the units digit of $5 \times 5 \times 5 \times 5$, which is $625$, so the units digit is $\boxed{5}$.
The answer is: 5
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the units digit when $5^4$ is multiplied out?

### Answer:
