Question 32920
You are doing fine when you wrote:
(m^8-5)(m^8+5)=0
Therefore m^8=5 or m^8=-5
m=5^(1/8)= 1.223..
You could also say m^8+5=0
So, m^8=-5.  This is true only
if m is a complex number.
I'm not saying the above is the only 
way you could solve m^16-25=0; it depends
on what level of mathematics you are studying.
But your writing (m^8-5)(m^8+5)=0 is the way
to start.
Cheers,
Stan H.