How many $3$-inch-by-$5$-inch photos will it take to completely cover the surface of a $3$-foot-by-$5$-foot poster?

$\text{(A) }24\qquad\text{(B) }114\qquad\text{(C) }160\qquad\text{(D) }172\qquad\text{(E) }225$
1. **Convert the dimensions of the poster from feet to inches:**
   - The poster is \(3\) feet by \(5\) feet.
   - Since \(1\) foot is equal to \(12\) inches, we convert the dimensions:
     \[
     3 \text{ feet} = 3 \times 12 = 36 \text{ inches}
     \]
     \[
     5 \text{ feet} = 5 \times 12 = 60 \text{ inches}
     \]
   - Therefore, the poster is \(36\) inches by \(60\) inches.

2. **Calculate the area of the poster:**
   - The area of the poster is:
     \[
     \text{Area of poster} = 36 \text{ inches} \times 60 \text{ inches} = 2160 \text{ square inches}
     \]

3. **Calculate the area of one photo:**
   - Each photo is \(3\) inches by \(5\) inches.
   - The area of one photo is:
     \[
     \text{Area of one photo} = 3 \text{ inches} \times 5 \text{ inches} = 15 \text{ square inches}
     \]

4. **Determine the number of photos needed to cover the poster:**
   - To find the number of photos required, divide the area of the poster by the area of one photo:
     \[
     \text{Number of photos} = \frac{\text{Area of poster}}{\text{Area of one photo}} = \frac{2160 \text{ square inches}}{15 \text{ square inches}} = 144
     \]

Conclusion:
\[
\boxed{144}
\]