The bag contains 5 red and 3 blue balls, so the total number of balls is \( 5 + 3 = 8 \). The probability of drawing a red ball is:
\[
P(\text{red}) = \frac{\text{Number of red balls}}{\text{Total balls}} = \frac{5}{8}
\]
Thus, the probability is:
\[
\boxed{\frac{5}{8}}
\]