Answer
The paintings are $15683$ years old.
Work Step by Step
The half life for carbon is 5730 years.
so, $k=\dfrac{\ln 2}{5730}$
$C=C_0e^{-\dfrac{\ln 2}{5730}t}$
Now, at $C=0.15 C_0$
$0.15 C_0=C_0e^{-\dfrac{\ln 2}{5730}(t)}$
so, $t \approx 15683$
This means that the paintings are $15683$ years old.