#### Answer

$41$ years

#### Work Step by Step

The half life for carbon is 5730 years.
so, $C=C_0e^{kt}$
$(1/2)C_0=C_0e^{5700k} \implies k=-0.0001216$
Now, $0.995 C_0=C_0e^{-0.0001216t}$
$C=C_0e^{-\dfrac{\ln 2}{5730}(5000)}$
s$\implies \ln (0.995)=-0.0001216 t$
Thus, $t \approx 41$ years