The fifth was discovered yesterday in Wainfleet, 8km from Skegness.
Graffiti was sprayed on the bodies of two of the whales on the beach near Gibraltar Point in Skegness.
Messages reading “Fukushima RIP”, “CND” and “man’s fault” have been written in white lettering on the bodies of the whales.
East Lindsey District Council has said it may be a “few days” before the whales are removed, as it needs to be granted formal permission by the Marine Management Organisation.
The pod has been linked to 12 whales that stranded and died in the Netherlands and Germany earlier this month.
Richard Johnson of the UK Coastguard said: “We believe the three whales at Skegness died at sea and then washed ashore.
"We are advising members of the public to stay away from the beach.
“We have informed the receiver of wreck and we are expecting an officer from the Zoological Society of London to attend the scene and carry out tests.”