Choice B is correct. The second equation in the given system is $y = 5 x^{2} + 4$ . Substituting $5 x squared plus 4$ for $y$ in the first equation of the given system yields $5 x^{2} + 4 = 5 x + 4$ . Subtracting $4$ from both sides of this equation yields $5 x squared equals 5 x$ . Subtracting $5 x$ from both sides of this equation yields $5 x^{2} - 5 x = 0$ . Factoring out a common factor of $5 x$ from the left-hand side of this equation yields $5 x (x - 1) = 0$ . It follows that $5 x equals 0$ or $x - 1 = 0$ . Dividing both sides of the equation $5 x equals 0$ by $5$ yields $x equals 0$ . Substituting $0$ for $x$ in the equation $y = 5 x + 4$ yields $y = 5 (0) + 4$ , or $y equals 4$ . Therefore, a solution to the given system of equations is the ordered pair $left parenthesis 0 comma 4 right parenthesis$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.