To find the width of the rectangular prism, we can use the formula for the surface area \( S \) of a rectangular prism:
\[ S = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width, and
- \( h \) is the height.
Given the surface area \( S = 160 \) square centimeters, length \( l = 10 \) centimeters, and height \( h = 5 \) centimeters, we can substitute these values into the formula:
\[ 160 = 2(10w + 10 \cdot 5 + 5w) \]
Calculating \( 10 \cdot 5 \):
\[ 10 \cdot 5 = 50 \]
Now substituting this back into the equation:
\[ 160 = 2(10w + 50 + 5w) \]
Simplifying further:
\[ 160 = 2(15w + 50) \]
Dividing both sides by 2:
\[ 80 = 15w + 50 \]
Subtracting 50 from both sides:
\[ 80 - 50 = 15w \]
\[ 30 = 15w \]
Dividing both sides by 15 to solve for \( w \):
\[ w = \frac{30}{15} = 2 \]
Thus, the width of the prism is \( 2 \) centimeters.
Therefore, the answer is: A. 2 centimeters