The agency had been assisting the 'Sea Breeze' since it began to take on water, and the RNLI was also called and successfully too six people off the ship.
A spokesman for the Maritime and Coastguard Agency said: "The Sea Breeze has been towed to St Austell Bay where repair work will take place to its damaged hull.
"Our surveyors will examine the cargo vessel to ensure it meets UK and international safety standards, once the repair work has been completed by the owners and operators ."
Lizard and Falmouth RNLI Lifeboats and a rescue helicopter from RNAS Culdrose attempted to pump water out of vessel with their own pumps. Other merchant vessels, who heard the mayday relay broadcast from Falmouth Coastguard, also stood by in case they were required.
Alex Greig, Falmouth Coastguard Watch Manager says: "We received the mayday broadcast from the 'Sea Breeze' at 7.00 am and were able to get lifeboats and the helicopter on scene quickly, along with other vessels that were in the vicinity. The lifeboats and helicopter pumped water off the cargo vessel, whilst HMS Tyne was on its way with commercial pumps. However, unfortunately, the smaller pumps could not keep up with the ingress of water and the crew had to abandon ship at 8.40 am. Five of the crew are now safely ashore. A couple of them have minor injuries. The captain has remained on scene on board HMS Tyne to help with the salvage operation.