Answer
about $63,000$ years
Work Step by Step
When $ 99.95\%$ of $A$ has decayed, the amount that remains is $0.0005A$.
We want the $t$ for which
$0.0005A=A(0.999879)^{t}$
$0.0005=(0.999879)^{t}$
$\log 0.0005=t\cdot\log 0.999879$
$ t=\displaystyle \frac{\log 0.0005}{\log 0.999879}\approx\ 62813.575$
or, about $63,000$ years
