There is a power of $2$ with a natural exponent, which can be represented as several different powers of $3$ with whole non-negative exponent. For example, $2^{2}=3^{1}+3^{0}$ or $2^{8}=3^{5}+3^{2}+3^{1}+3^{0}$.
There is also a power of $3$ with a natural exponent, which can be represented as several different powers of $4$ with whole non-negative exponent. For example, $3^{4}=4^{3}+4^{2}+4^{0}$.
However, is there any power of $4$ with natural exponent that can be represented as sum of several different powers of $5$ with whole non-negative exponent?