We report on searches of the globular cluster Terzan 5 for low-luminosity and accelerated radio pulsars using the 64-m Parkes radio telescope. One new millisecond pulsar, designated PSR J1748−2446C, was discovered, having a period of 8.44 ms. Timing measurements using the 76-m Lovell radio telescope at Jodrell Bank show that it is a solitary pulsar and lies close to the core of the cluster. We also present the results of timing measurements which show that the longer period pulsar PSR J1748−2444 (formerly known as PSR B1744−24B) lies 10 arcmin from the core of the cluster and is unlikely to be associated with the cluster. We conclude that there are further pulsars to be detected in the cluster.