A rectangular piece of paper measuring 8 cm by 5 cm is to have its length and width reduced by the same amount. What is the area of the paper after the reduction?

The original length $L_0 = 8$ cm.
The original width $W_0 = 5$ cm.

Let the equal amount by which both the length and width were reduced be $x$ cm.
For the dimensions to remain positive, $x$ must be less than the smallest original dimension, so $0 < x < 5$.

The new length $L = (L_0 - x) = (8-x)$ cm.
The new width $W = (W_0 - x) = (5-x)$ cm.

The area of a rectangle is given by $A = L \times W$.

The problem asks to "Determine the area of the drawing paper", implying a specific numerical value. However, the value of $x$ (the amount by which the dimensions were reduced) is not provided in the question. Without knowing the value of $x$, or the new area, it is not possible to determine a numerical value for the area of the drawing paper.

Therefore, the problem is incomplete as presented.