When you see a square root, and you are asked about the domain, take care that the function under the square root is non-negative.

So, in this case these two inequalities must be held:

5-3x > 0,    (1)   and
x+1   = 0.   (2).

Notice that in (1) I wrote the strong inequality.
It is because we have  in the denominator.


Now, from (1),  5 > 3x,  x < .

From (2),  x >= -1.


So, the answer is -1 <= x < .


It is the semi-segment  [-1, ).


The domain is the semi-segment  [-1, ).