Well, I'm not done yet. Am I on the right track?
NOT yet
First of all you need to find the values of x for which all the square roots are possible.i.e quantities under the square root signs must be non-negative.
On taking the intersection of the above conditions you will get
which can be said to be the domain of the inequality.
Now the solutions you obtain by solving
i.e
i.e
Therefore the values of x satisfying both the inequalities are
which must satisfy .
Therefore the answer to the given question must be [5,7]