jmc

By the definition of $f(x)$, we have $f(3)=3a+3b+2$, so if we find $3a+3b$, we can find $f(3)$. Since $f(1)=a+b+2$ (by the definition of $f(x)$) and $f(1)=5$, we have $a+b+2=5$, so $a+b=3$. Multiplying this by 3 gives $3a+3b=9$, so $f(3)=3a+3b+2=9+2=\boxed{11}$. Notice that we didn't even need the information about $f(2)$!