If (x+5)^4 = 81,
then (x+5)^2 = ± sqrt(81), so
(x+5)^2 = ±9
Focusing on (x+5)^2 = 9 for the two real roots, we have
(x+5)^2 = 9
x+5 = ± sqrt(9)
x+5 = ± 3
x+5 = 3 gives you x = -2
x+5 = -3 gives you x = -8
There are two complex roots too, but I'm not sure if you're studying that too. If so, then you'd solve (x+5)^2 = -9:
x+5 = ± sqrt(-9)
x+5 = ±3i
x = 5 ± 3i as the two complex roots.