It is a real but an irrational number
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No, it is not even a real number. The square root of negative 5 is the square root of 5, times i.
X is greater than 5. If X were equal to 5, X-5 would be 0 which has no real square root. If X were 4, X-5 would be -1 which has no real square root, and so on.
The square root of a positive number results in a positive number. For example, the square root of 25 is 5. * * * * * Not true! There are two real square roots for every positive number: one positive and one negative. -5 is as much a square root of 25 as +5 is. However, the positive root is the principal root and so is often presented as the only root.
There is no real number [square] root of a negative number. There is a real cube root and a real fiftth root etc, but root, by itself, implies square root.
It is real and irrational.