What is the domain of the function y=2then this is under a square root x-5

The domain is {x∈R|x≥5}. 
This means all real numbers that are greater than or equal to 5.

The domain is the set of x-values.  To get real-number answers, x cannot be less than 5; if you use a number less than 5 in x-5, you end up with a negative number under the square root.  We cannot take the square root of a negative number using only real numbers.