To find the probability that both fruits drawn are apples, we can use combinatorial counting.
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Total fruits in the basket:
- 5 apples + 3 pears = 8 fruits.
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Total ways to choose 2 fruits from 8: \[ \text{Total ways to choose 2 fruits} = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28. \]
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Total ways to choose 2 apples from 5: \[ \text{Total ways to choose 2 apples} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10. \]
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Probability of choosing 2 apples: \[ \text{Probability} = \frac{\text{Ways to choose 2 apples}}{\text{Total ways to choose 2 fruits}} = \frac{10}{28}. \]
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Simplifying the fraction: \[ \frac{10}{28} = \frac{5}{14}. \]
Thus, the probability that both fruits taken are apples is \(\frac{5}{14}\).