Answer
The missing power is $\frac{2}{3}$.
Work Step by Step
RECALL:
$a^m \cdot a^n = a^{m+n}$
Let x = missing/unknown power
Use the rule above to obtain:
$5^{\frac{1}{3}} \cdot 5^{x} = 5
\\5^{\frac{1}{3}} \cdot 5^{x} = 5^1
\\5^{\frac{1}{3}+x}=5^1$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$\frac{1}{3} + x = 1
\\x = 1 - \frac{1}{3}
\\x = \frac{3}{3} - \frac{1}{3}
\\x = \frac{2}{3}$
