Old contest problem. Diophantine equation?

[steiner1745]

Find all non-negative integers such that
5^x + 7^y = 2^z.
Two solutions are 0,0,1 and 2,1,5.
Are there any others?

 

[jay cee]

searched for all combinations of x and y b/w 1 and 40 using computer. didn't find any, so if there are any others, they're huge numbers.