Answer
$g=9.6m/s^2$
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 $g$ yields $$\frac{T}{2\pi}=\sqrt{\frac{l}{g}}$$ $$\frac{T^2}{4\pi^2}=\frac{l}{g}$$ $$g=\frac{4\pi^2l}{T^2}$$ Substituting known values of $l=2.5m$ and $T=3.2s$ yields a gravity value of $$g=\frac{4\pi^2(2.5m)}{(3.2s)^2}=9.6m/s^2$$
