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To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest perfect square greater than 5 and lesser than 7.
5 is closest to the perfect square 4, and 7 is closest to the perfect square 9. However, 4 is not a valid answer since its square root is 2 which is not between 5 and 7.
The next perfect square greater than 5 is 9. The square root of 9 is ≠3, which is between 5 and 7.
Therefore, the answer is d. 26.