The Howe family recently bought a house. The house has a $15-$year, $$217,208\mathrm{.}00$ mortgage with monthly payments and a nominal interest rate of $5\mathrm{.}7$ percent. What is the total dollar amount of interest the family will pay during the first $5$ years of their mortgage? $($Assume that all payments are made at the end of the month.$)$

$$50,828\mathrm{.}90$

$$53,828\mathrm{.}90$

$$52,828\mathrm{.}90$

$$54,828\mathrm{.}90$

$$51,828\mathrm{.}90$