High-fidelity two-qubit gates are essential for the realization of large-scale quantum computation and simulation. Tunable coupler design is used to reduce the problem of parasitic coupling and frequency crowding in many-qubit systems and thus thought to be advantageous. Here we design an extensible 5-qubit system in which center transmon qubit can couple to every four near-neighboring qubits via a capacitive tunable coupler and experimentally demonstrate high-fidelity controlled-phase (CZ) gate by manipulating central qubit and one near-neighboring qubit. Speckle purity benchmarking and cross entropy benchmarking are used to assess the purity fidelity and the fidelity of the CZ gate. The average purity fidelity of the CZ gate is 99.69±0.04% and the average fidelity of the CZ gate is 99.65±0.04%, which means that the control error is about 0.04%. Our work is helpful for resolving many challenges in implementation of large-scale quantum systems.