The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding, and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of labeled crotonic acid. The ability to correct each error was verified by tomography of the process. The use of error correction for benchmarking quantum networks is discussed, and we infer that the fidelity achieved in our experiment is sufficient for preserving entanglement.