It follows the death of a beached whale in Hunstanton, Norfolk, on Friday and the discovery of three carcasses near Skegness over the weekend.
The sperm whales are believed to be from a pod spotted off the Norfolk coast.
The fifth whale was found at Wainfleet, Lincolnshire, on Monday afternoon, the Maritime and Coastguard Agency reported.
It was found on the site of a former bombing range, and warnings have been issued for people to stay away.
The Lincolnshire Wildlife Trust tweeted: "There is no public access to the area and it is extremely dangerous with tidal creeks and the potential for unexploded ordinance. Many of the lanes to the marshes are private and not accessible."
Why do sperm whales wash up on beaches?
Marine biologists were using a probe to examine one of the Skegness whales earlier on Monday when there was a "huge blast of air", said BBC reporter David Sykes.
The letters CND had also been spray-painted by someone on the whale's tail.
CND (Campaign for Nuclear Disarmament) said the action was not carried out by the organisation at a national level.
The word "fukushima" - presumably a reference to the stricken Japanese nuclear power station - was also written on the side of the whale's body.
One of the Skegness whales is at the end of Lagoon Walk, with the other two towards Gibraltar Point.
They have been cordoned off to prevent crowds of people touching the carcasses.
People are also being prevented from going too close to the Hunstanton whale.
A fifth sperm whale has washed up on the east coast of England.