1. **State the problem:** Simplify the expression $5 \left( \csc \sqrt{x} \right)^3$. 2. **Recall the definition:** The cosecant function is $\csc \theta = \frac{1}{\sin \theta}$. 3. **Rewrite the expression:** $$5 \left( \csc \sqrt{x} \right)^3 = 5 \left( \frac{1}{\sin \sqrt{x}} \right)^3$$ 4. **Simplify the power:** $$= 5 \cdot \frac{1}{\sin^3 \sqrt{x}} = \frac{5}{\sin^3 \sqrt{x}}$$ 5. **Final answer:** $$\boxed{\frac{5}{\sin^3 \sqrt{x}}}$$ This is the simplified form of the given expression, where the cosecant cubed is expressed as the reciprocal of sine cubed of the square root of $x$.