What is the units digit when $5^4$ is multiplied out?
The units digit of any positive integer power of 5 is $\boxed{5}$.

(Note: this claim may be proved by induction, since the units digit of $5n$ is 5 whenever the units digit of $n$ is 5.)
5
Level 2
Number Theory
Problem: What is the units digit when $5^4$ is multiplied out?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the units digit of a number, we only need to consider the last digit of that number. The units digit of powers of 5 is consistent. Specifically, when calculating powers of 5, the last digit remains 5 regardless of the exponent. 

For example:
- $5^1 = 5$ (units digit is 5)
- $5^2 = 25$ (units digit is 5)
- $5^3 = 125$ (units digit is 5)
- $5^4 = 625$ (units digit is 5)

This pattern shows that the units digit of $5^n$ for any positive integer $n$ is always 5. 

Since we are multiplying $5^4$ by 1 (as it is the only number being considered), the units digit of the result remains unchanged. Therefore, the final answer is 5.<|END_OF_LATENT|> The final answer is $5$.