John Doe recently acquired $500$ shares of TECorp at $$54\mathrm{.}00$ per share and has opted to engage in writing covered calls against these holdings. Consequently, he has sold five TECorp calls at the present market price of $$4\mathrm{.}75.$ These calls possess a remaining term of three months until expiration and feature a strike price of $$57.$ Additionally, the stock yields a quarterly dividend of $$0\mathrm{.}50$ per share, with the next dividend anticipated in roughly a month.

$1.$ Calculate the total profit that John will realize if the stock ascends to $$57$ per share by the expiration date of the calls.