Yes it is. There is no fraction which, when cubed, equates to 5. Consider n = p/q where p and q are integers expressed in lowest terms (they are relatively prime). If n3 = 5, then p3 / q3 = 5. This equates to an integer if and only if q3 = 1 meaning q = 1 or if p3 is divisible by q3. The latter is impossible since p and q are relatively prime. Thus, for n to be the cube root of 5 and be rational, it must be an integer. No integer cubes to 5 (1, 8, ...). Thus, the cube root of 5 is irrational.
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The cube root of 125 is 5 -- that is 5*5*5 = 125
An example is the square root of a number. Ex: square root of 2. This is 1 example, not the main one. Any cube root or square root which doesn't give a perfect number is an irrational number. Ex; square root and cube root of 5, since their answer will be 2.24 and 1.70 which are not perfect numbers like square roots of 25 and 64 or cube roots of 27 and 216.
The cube root of 125 is 5; the square of 5 is 25.
5 times the cube root of 54 = 18.8988157
the cube root of 25