Saying that x[sup]y[/sup] = 1 for complex numbers is really saying that e[sup]y ln(x)[/sup] = 1. If we write x = r e[sup]i theta[/sup] and y = a + bi, this means that
exp((a + bi) ( ln r + i theta + 2 pi i n) ) = 1
exp((a ln r - b theta - 2 pi b n) + i (b ln r + a theta + 2 pi a n) ) = 1
This equation will hold if
a ln r - b theta - 2 pi b n = 0 and
b ln r + a theta + 2 pi a n = 2 pi m
for some integer values of m and n. In your case, 5[sup] 2 pi i / ln 5[/sup], you have r = 5, theta = 0, a = 0, b = 2 pi / ln 5; this works for n = 0, m = 1.
In summary: your math is correct, and it’s not true that x[sup]y[/sup] = 1 implies that |x| = 1, since you can play fast & loose with the values of m & n your equation is true for.
I hope this helps; I have a feeling I didn’t explain this all that well, so other attempts are probably welcome.