Step 1: Look at what multiplying by 5 does to the last digit.
Instead of proving this by induction, we can reason directly about last digits. When two numbers are multiplied, the last digit of the product depends only on the last digits of the two numbers being multiplied.
Step 2: Write $5^n$ as repeated multiplication by 5.
\[ 5^n = 5 \times 5 \times 5 \times \cdots \times 5 \quad (n \text{ times}) \]
Start with $5^1 = 5$, which ends in 5.
Step 3: Multiply a number ending in 5 by 5 again.
Take any number that ends in 5, say it looks like $10k + 5$ for some whole number $k$ (this is just the general way to write "a number ending in 5").
Multiply it by 5:
\[ (10k + 5) \times 5 = 50k + 25 = 10(5k + 2) + 5 \]
This result is again of the form $10(\text{something}) + 5$, so it also ends in 5.
Step 4: Chain this fact for every power.
Since $5^1$ ends in 5, multiplying it by 5 to get $5^2$ keeps the last digit 5. Multiplying $5^2$ by 5 to get $5^3$ keeps it 5 again, and this repeats for every further power.
So no matter how many times we multiply by 5, the last digit never changes from 5.
Step 5: Final Answer.
For every natural number $n$, $5^n$ ends with the digit 5, so option (B) is correct.
\[ \boxed{5} \]