Determine the total number of pens and the probability of drawing a blue pen first.

There are 5 red pens and 3 blue pens.
Total number of pens is $5 + 3 = 8$.
The probability of drawing a blue pen first is the number of blue pens divided by the total number of pens.

$$P(\text{1st pen is blue}) = \frac{\text{Number of blue pens}}{\text{Total number of pens}} = \frac{3}{8}$$

After drawing one blue pen, there are now $3 - 1 = 2$ blue pens left.
The total number of pens remaining is $8 - 1 = 7$.
The probability of drawing a second blue pen, given the first was blue, is:

$$P(\text{2nd pen is blue} | \text{1st pen is blue}) = \frac{\text{Number of blue pens remaining}}{\text{Total number of pens remaining}} = \frac{2}{7}$$

To find the probability that both pens are blue, multiply the probabilities from Step 1 and Step 2.

$$P(\text{Both pens are blue}) = P(\text{1st pen is blue}) \times P(\text{2nd pen is blue} | \text{1st pen is blue})$$ $$P(\text{Both pens are blue}) = \frac{3}{8} \times \frac{2}{7}$$ $$P(\text{Both pens are blue}) = \frac{3 \times 2}{8 \times 7}$$ $$P(\text{Both pens are blue}) = \frac{6}{56}$$

Simplify the fraction:

$$P(\text{Both pens are blue}) = \frac{3}{28}$$

The probability that both pens are blue is $\frac{3}{28}$.