Introduction:
To find the domain of the given function f(x) = √log(5x-x^2/6) at the points (2,3) and (0,5) and also the set of values for which the function is defined.

Calculations:
The domain of the function f(x) can be determined by considering the following conditions:

1. The argument of the logarithmic function must be greater than zero, i.e., 5x - x^2/6 > 0.

2. The argument of the square root function must be greater than or equal to zero, i.e., log(5x - x^2/6) ≥ 0.

Domain at point (2,3):

1. 5x - x^2/6 > 0
⇒ x(5-x/6) > 0
⇒ x ∈ (0, 6) (since 5-x/6 is negative in (0,5) and positive in (5,6))

2. log(5x - x^2/6) ≥ 0
⇒ 5x - x^2/6 ≥ 1
⇒ -x^2 + 30x - 6 ≥ 0
⇒ x ∈ (-∞, 0] U [5, ∞)

Therefore, the domain of f(x) at (2,3) is the intersection of the above two sets, i.e., f(x) is defined for x ∈ (5, 6).

Domain at point (0,5):

1. 5x - x^2/6 > 0
⇒ x(5-x/6) > 0
⇒ x ∈ (-∞, 0) U (0, 6) (since 5-x/6 is negative in (0,5) and positive in (-∞,0) U (5,6))

2. log(5x - x^2/6) ≥ 0
⇒ 5x - x^2/6 ≥ 1
⇒ -x^2 + 30x - 6 ≥ 0
⇒ x ∈ (-∞, 0] U [5, ∞)

Therefore, the domain of f(x) at (0,5) is the intersection of the above two sets, i.e., f(x) is defined for x ∈ (0, 6).

Domain of the function:
Combining the above two sets, we get the domain of the function f(x) as f(x) is defined for x ∈ (5, 6).

Conclusion:
The domain of the function f(x) = √log(5x-x^2/6) at the point (2,3) is (5,6), at the point (0,5) is (0,6) and the domain of the function f(x) is (5,6).