Given the function, $f(x)=-0\mathrm{.}9x^2+1\mathrm{.}7x+2\mathrm{.}5,$ using the Fixed$-$Point Iteration Method, where the initial value of $x=5,$ the approximate root after $5$ iterations is:

$($Test if $x=5$ converge to a solution or not, show all your work on handwritten submission$)$

$2\mathrm{.}86743$

$2\mathrm{.}88202$

$2\mathrm{.}65745$

$3\mathrm{.}09344$