The US Navy said four of the injured sailors were medically evacuated to a hospital in Singapore with non-life threatening injuries.
The fifth sailor did not need further medical attention.
A multinational search and rescue effort involving Singapore, Malaysia, Indonesia and the US is underway to locate the missing sailors.
After the collision, the Mc Cain sailed under its own power and headed to port at Changi Naval Base in Singapore.
The Singapore government said no crew were injured on the Liberian-flagged Alnic, which sustained damage to a compartment at the front of the ship some 23 feet above its waterline.