think of it this way:

we have and

Note that 5 is less than twice 3, while 11 is more than twice 5. in other words, has the task of increasing the base 5 a larger magnitude (relatively speaking) than has to do for 3. is larger

this is a more intuitive approach. which i suppose is the level of thinking this problem requires, since it is elementary/middle school math. there are more rigorous proofs, i'm sure