Answer:
[tex]\large\boxed{D.\ a^2+2ah+h^2+3a+3h+5}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2+3x+5\\\\f(a+h)\to\text{exchange x to (a + h)}:\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]
