Step 1: Score the primary tumor (T). In the TNM staging of oral carcinoma, T1 is a tumor 2 cm or smaller, T2 is 4 cm or smaller, and T3 is larger than 4 cm. The gum tumor here is 5 cm, which is larger than 4 cm, so it is T3.
Step 2: Score the nodes (N). N2c is defined as metastasis in bilateral or contralateral lymph nodes, none larger than 6 cm in greatest dimension. The node here is contralateral and 2 cm (under 6 cm), so it falls under the N2 group, giving N2.
Step 3: Score metastasis (M). There is no distant metastasis, so it is M0.
Step 4: Combine. T3 + N2 + M0 = T3N2M0. This is the correct answer. T2N2M0 is wrong because 5 cm exceeds the 4 cm cut-off for T2. T1N2M0 is wrong for the same size reason. T3N3M0 is wrong because N3 requires a node larger than 6 cm, but this node is only 2 cm.