Step 1: Identify compounds with NO sp\(^3\) carbons.
sp\(^3\) carbon requires 4 single bonds (tetrahedral). Compounds with only sp or sp\(^2\) carbons have no sp\(^3\) carbon.
Step 2: Check each compound.
I (Acetone): CH\(_3\)-CO-CH\(_3\) -- the two CH\(_3\) carbons are sp\(^3\). II (Acetic acid): CH\(_3\)-COOH -- the CH\(_3\) carbon is sp\(^3\). III (Buta-1,3-diene): CH\(_2\)=CH-CH=CH\(_2\) -- all four carbons are sp\(^2\), no sp\(^3\). IV (Propyne): CH\(_3\)-C\(\equiv\)C-H -- the CH\(_3\) carbon is sp\(^3\). V (Naphthalene): all aromatic carbons are sp\(^2\), no sp\(^3\). Only III and V have no sp\(^3\) carbons. \[ oxed{III ext{ and } V} \]