Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies.