Evaluate cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5 . 5 to the power of negative 1 over 6 5 to the power of 3 over 2 5 to the power of 5 over 2 5 to the power of negative 5 over 6

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Convert everything to exponential form, and then use the rules for working with exponents. 
cube root of 5 = 5^⅓ 
²√5 = 5^½ 
cube root of 5 to the power of 5 =5^(5/3) 
Therefore, cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5 =  5^(⅓ + ½ - (5/3)) = 5^{(2 + 3 - 10)/6} = 5^(-5/6)

The answer should be 5 to the power of negative 5 over 6