Allen flips a fair two sided coin and rolls a fair $6$ sided die with faces numbered $1$ through $6$. What is the probability that the coin lands on heads and he rolls a number that is a multiple of $5$?

$\textbf{(A) }\dfrac1{24}\qquad\textbf{(B) }\dfrac1{12}\qquad\textbf{(C) }\dfrac16\qquad\textbf{(D) }\dfrac14\qquad\textbf{(E) }\dfrac13$
1. **Identify the events:**
   - Let \( A \) be the event that the coin lands on heads.
   - Let \( B \) be the event that the die shows a number that is a multiple of 5.

2. **Determine the probability of each event:**
   - The probability of the coin landing on heads, \( P(A) \), is \( \frac{1}{2} \) because the coin is fair.
   - The die has numbers 1 through 6, and the only number that is a multiple of 5 is 5. Therefore, the probability of rolling a 5, \( P(B) \), is \( \frac{1}{6} \).

3. **Calculate the combined probability:**
   - Since the coin flip and the die roll are independent events, the probability of both events occurring is the product of their individual probabilities:
     \[
     P(A \cap B) = P(A) \cdot P(B) = \frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}
     \]

4. **Conclusion:**
   - The probability that the coin lands on heads and the die shows a number that is a multiple of 5 is \( \boxed{\frac{1}{12}} \).