how to work out root 5 of 0.035

You're going to find the fifth root of 0.035?

First, use the calculator.

If you don't have one, calculate:
Set x0=0.2
calculate
x1=x0-(x0^5-0.035)/(5x0^4)
Start with x0=0.55, and calcuate x1.
Repeat by replacing x0 by x1 until the number stabilizes to the accuracy you need, or 0.511462278313015