Question 32920
You did all the work. It looks OK to me
All you need to add is the las steps
(m^8-5) 
(m^8+5)=0
m^8-5=0 
m^8+5=0
m^8= 5  
m^8= -5
{{{m = 5^(1/8)}}}
{{{m = (-5)^(1/8)}}}
check by substitution
{{{m^16 = 25}}}
{{{(5^(1/8))^16 = 25}}}
{{{5^(16/8) = 25}}}
{{{5^2 = 25}}}
{{{25 = 25}}}
and
{{{((-5)^(1/8))^16 = 25}}}
{{{(-5)^(16/8) = 25}}}
{{{(-5)^2 = 25}}}
{{{25 = 25}}}