Five of 19 pilot whales that beached at Noordhoek Beach in Cape Town were taken out to sea on Sunday afternoon.
The NSRI's Craig Lambinon said one of them had already re-beached in Simonstown.
The five had been placed on trailers at Noordhoek Beach and transported to the Simonstown naval base, before being taken out to sea.
Lambinon says they were witnessed by following boats to be swimming strongly in False Bay at around 7 pm on Sunday night.
He said nine other whales had been humanely euthanised, while another five had died naturally.
The 19, mostly adult, whales beached on Sunday morning.