Answer
$\$ 23,763.28$
Work Step by Step
A sinking fund is an account earning compound interest into which you make periodic deposits. $\\$
$FV=PMT\displaystyle \cdot\frac{(1+i)^{n}-1}{i}\\\\$
In the meantime, the amount that already exists in the account earns interest (compound formula)
$FV_{0}=PV(1+i)^{n}$
----------------
Here, $\\$
$t=10$ years$,\\$
m= $12 \ \ \ $compounding periods per year,$\\$
$n=mt=120 \ \ $(total number of periods)$\\$
$\displaystyle \mathrm{i}=\frac{r}{m}=\frac{0.05}{12} \ \ $(rate per compounding period$)\\$
$PMT=100\ \ \ $( payment at the end of each period)$\\\\$
$FV=100\displaystyle \cdot\frac{(1+\frac{0.05}{12})^{120}-1}{\frac{0.05}{12}}\approx\$ 15,528.23$
$-----------$
Meanwhile, the PV=5000 earns interest and grows to$\\\\$
$FV_{0}=5000(1+\displaystyle \frac{0.05}{12})^{120}\approx\$ 8,235.05\\\\$
$Total\approx\$ 23,763.28$
