To find the consecutive whole numbers that the square root of 26 falls between, we need to determine the square roots of the whole numbers surrounding 26.
We know that:
- \(5^2 = 25\)
- \(6^2 = 36\)
Therefore, we can infer that:
\[ 5 < \sqrt{26} < 6 \]
So, the consecutive whole numbers that \(\sqrt{26}\) falls between are \(5\) and \(6\).