Step 1: Recall what an electron withdrawing group means.
An electron withdrawing group is a substituent that pulls electron density away from the rest of the molecule. This may happen through the \(-I\) effect, the \(-M\) effect, or both. Such groups generally reduce electron density on adjacent atoms or aromatic rings.
Step 2: Examine the group \(-CN\).
The cyano group \(-CN\) is strongly electron withdrawing. It withdraws electron density because of the highly electronegative nitrogen and the multiple bond system. Therefore, \(-CN\) is definitely an electron withdrawing group.
Step 3: Examine the groups \(-NO_2\), \(-COOH\), and \(-COOR\).
The nitro group \(-NO_2\) is one of the strongest electron withdrawing groups due to both inductive and resonance effects. Similarly, \(-COOH\) and \(-COOR\) contain a carbonyl group, which strongly withdraws electron density. So all these groups are electron withdrawing in nature.
Step 4: Now analyze \(-OCH_3\).
The methoxy group \(-OCH_3\) shows a weak \(-I\) effect because oxygen is electronegative, but it also has lone pairs that can donate electron density by resonance \((+M\) effect\().\) In many organic chemistry contexts, especially in aromatic systems, \(-OCH_3\) behaves as an electron donating group overall.
Step 5: Compare all options.
Among the given groups, \(-CN\), \(-NO_2\), \(-COOH\), and \(-COOR\) are electron withdrawing, whereas \(-OCH_3\) is not treated as an electron withdrawing group in the usual overall sense.
Step 6: Identify the required option.
Since the question asks for the group that is not electron withdrawing, the correct choice must be the methoxy group.
Step 7: State the final answer.
Hence, the group which is not an electron withdrawing group is:
\[
\boxed{-OCH_3}
\]
which matches option \((5)\).