1. **State the problem:** We need to find the probability that a card drawn from a standard deck of 52 cards is either a black card or a 5. 2. **Recall the formula for probability of union of two events:** $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ where $A$ is the event "card is black" and $B$ is the event "card is a 5". 3. **Calculate each probability:** - Total cards: 52 - Number of black cards: 26 (clubs and spades) - Number of 5s: 4 (one in each suit) - Number of black 5s: 2 (5 of clubs and 5 of spades) So, $$P(A) = \frac{26}{52} = \frac{1}{2}$$ $$P(B) = \frac{4}{52} = \frac{1}{13}$$ $$P(A \cap B) = \frac{2}{52} = \frac{1}{26}$$ 4. **Apply the formula:** $$P(A \cup B) = \frac{1}{2} + \frac{1}{13} - \frac{1}{26}$$ 5. **Find common denominator and simplify:** $$\frac{1}{2} = \frac{13}{26}, \quad \frac{1}{13} = \frac{2}{26}$$ So, $$P(A \cup B) = \frac{13}{26} + \frac{2}{26} - \frac{1}{26} = \frac{14}{26}$$ 6. **Simplify the fraction:** $$\frac{14}{26} = \frac{\cancel{14}^{7}}{\cancel{26}^{13}} = \frac{7}{13}$$ **Final answer:** The probability that the card is a black card or a 5 is **$\frac{7}{13}$**.