Question 7173
You should use logarithms on this problem.

{{{0.8 = 5^n}}} Take the log of both sides:
{{{log(0.8) = nlog(5)}}} Divide both sides by log(5)
{{{n = log(0.8)/log(5)}}} Do this in your calculator for more accuracy.
{{{n = -.09691/.69897}}}
{{{n = -.13865}}} Approximately

Use your calculator to check:

{{{5^-.13865 = 0.7999996}}}