Calculate the probability that both pens drawn are red.

There are 5 red pens and 3 blue pens, making a total of 8 pens.
The probability of drawing a red pen first is $\frac{5}{8}$.
After drawing one red pen without replacement, there are 4 red pens left and a total of 7 pens remaining.
The probability of drawing a second red pen is $\frac{4}{7}$.
The probability of both pens being red is:

$$P(\text{Both red}) = \frac{5}{8} \times \frac{4}{7} = \frac{20}{56} = \frac{5}{14}$$

The probability of drawing a blue pen first is $\frac{3}{8}$.
After drawing one blue pen without replacement, there are 2 blue pens left and a total of 7 pens remaining.
The probability of drawing a second blue pen is $\frac{2}{7}$.
The probability of both pens being blue is:

$$P(\text{Both blue}) = \frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28}$$

To find the probability that both pens are of the same color, add the probabilities of both being red and both being blue.

$$P(\text{Same color}) = P(\text{Both red}) + P(\text{Both blue})$$ $$P(\text{Same color}) = \frac{5}{14} + \frac{3}{28}$$

To add these fractions, find a common denominator, which is 28.

$$P(\text{Same color}) = \frac{5 \times 2}{14 \times 2} + \frac{3}{28}$$ $$P(\text{Same color}) = \frac{10}{28} + \frac{3}{28}$$ $$P(\text{Same color}) = \frac{10 + 3}{28} = \frac{13}{28}$$

The probability that both pens are of the same color is $\frac{13}{28}$.