7.219. $5^{1+x^{3}}-5^{1-x^{3}}=24$.

7.219. $5^{1+x^{3}}-5^{1-x^{3}}=24$.
Solution.

We have $5 \cdot 5^{x^{3}}-\frac{5}{5^{x^{3}}}-24=0 \Leftrightarrow 5 \cdot\left(5^{x^{3}}\right)^{2}-24 \cdot 5^{x^{3}}-5=0$. Solving this equation as a quadratic in terms of $5^{x^{3}}$, we get $5^{x^{3}}=-\frac{1}{5}$ (no solutions), or $5^{x^{3}}=5 \Rightarrow x^{3}=1, x=1$.

Answer: 1 .