Rebecca took out a fully amortizing $30$ year mortgage with the initial balance of $$5870.$ This mortgage has a fixed interest rate at $5\%.$ How much, in dollars, of Rebecca's first monthly payment was attributable to principal? In other words, what is Rebecca's principal payment in month one. Write the answer as a number rounded to two decimals $($e$.$g$.$ if you get $$500\mathrm{.}66666,$ write $500\mathrm{.}67).$