To find which function satisfies, f(5)=12, put x=5 for each function and check if the answer is 12.
[tex]\begin{gathered} f(x)=x-7 \\ f(5)=5-7 \\ =-2 \end{gathered}[/tex][tex]\begin{gathered} f(x)=5x+12 \\ f(5)=5\times5+12 \\ =37 \end{gathered}[/tex][tex]\begin{gathered} f(x)=x^2-13 \\ =5^2-13 \\ =25-13 \\ =12 \end{gathered}[/tex]Therefore, f(5)=12 is satisfied by the function
[tex]f(x)=x^2-13[/tex]