Choice D is correct. It's given that the function $f$ is defined by $f left parenthesis x right parenthesis equals 5 x squared$ . Substituting $8$ for $x$ in $f left parenthesis x right parenthesis equals 5 x squared$ yields $f left parenthesis 8 right parenthesis equals 5 left parenthesis 8 right parenthesis squared$ , which is equivalent to $f left parenthesis 8 right parenthesis equals 5 left parenthesis 64 right parenthesis$ , or $f left parenthesis 8 right parenthesis equals 320$ . Therefore, the value of $f left parenthesis 8 right parenthesis$ is $320$ .

Choice A is incorrect. This is the value of $f left parenthesis 8 right parenthesis$ if $f left parenthesis x right parenthesis equals 5 x$ .

Choice B is incorrect. This is the value of $f left parenthesis 8 right parenthesis$ if $f (x) = 5 (x + 2)$ .

Choice C is incorrect. This is the value of $f left parenthesis 8 right parenthesis$ if $f left parenthesis x right parenthesis equals left parenthesis 5 x right parenthesis left parenthesis 2 right parenthesis$ .