Step 1 :Let $f(x)=-3 x+5$
Step 2 :Substitute $x+3$ into the function $f(x)$ to find $f(x+3)$
Step 3 :$f(x+3) = -3*(x+3) + 5$
Step 4 :Simplify $f(x+3)$ to get $-3x - 4$
Step 5 :Final Answer: \(\boxed{-3x - 4}\)