Answer
$l=0.248m$
Work Step by Step
To find the period of the oscillations, note that if 5.0 swings are completed in 16s, one swing is completed in $16s/5.0=3.2s$, which is the period. Note that the formula relating the period with pendulum length and gravity is $$T=2\pi \sqrt{\frac{l}{g}}$$ Solving for $l$ yields $$\frac{T}{2\pi}=\sqrt{\frac{l}{g}}$$ $$\frac{T^2}{4\pi^2}=\frac{l}{g}$$ $$l=\frac{T^2g}{4\pi^2}$$ Substituting known values of $g=9.81m/s^2$ and $T=1.00s$ yields a length of $$l=\frac{(1.00s)^2(9.81m/s^2)}{4\pi^2}=0.248m$$
