The "relay" type needed would be called either "Motor Contactor" or "Motor Starter." These are designed and rated to handle the high starting current and the arcing at turn-off. As it happens, 5HP is a common size for air compressors so they are readily available.
Since the incoming power has both lines above ground, that is both are Hot, the starter must control both of them. The lowest cost and readily available approach would be a 3-phase, 5HP, 240v starter. I strongly recommend a starter with built-in thermal overloads. The thermal overloads function as an automatically- reset circuit breaker that senses current on each phase.
If you are buying from an Authorized Distributor or a large industrial supplier, you can specify the coil voltage you want, usually from 24V up to line voltage. As the devices are designed for industrial usage, they are designed for easy field repair and parts are readily available.
Both manually operated and electrically operated versions are made. The one you need, with a coil, is called a Magnetic Starter.
Try a Google search for: magnetic starter 5hp 230v 3ph
Cheers,
Tom