Five cards are drawn from a standard pack of 52 cards…

Step 1. With replacement. The draws are independent, so $X \sim B\left(5, \dfrac{1}{4}\right)$. $P(X = 2) = \binom{5}{2}\left(\dfrac{1}{4}\right)^2\left(\dfrac{3}{4}\right)^3 = \dfrac{270}{1024} \approx 0.2637$.

Step 2. Without replacement. $\binom{13}{2} = 78$, $\binom{39}{3} = 9139$ and $\binom{52}{5} = 2\,598\,960$. So $P(X = 2) = \dfrac{78 \times 9139}{2\,598\,960} = \dfrac{712\,842}{2\,598\,960} \approx 0.2743$.

Step 3. The difference. $0.2743 - 0.2637 \approx 0.0106$.

What it means. The two answers are close, because the sample is $5$ cards from a pack of $52$, a small part of the pack. They are not equal, because without replacement the draws are not independent.