"This is a message to David Cameron," says one of the gunmen, speaking in a British accent.
British warplanes, which were already attacking IS positions in Iraq, at the beginning of December began targeting the jihadists in Syria also.
The fighter says those who want to continue fighting "under the banner of Cameron" should ask themselves what would happen to them if they were to fall into IS hands.
He also says IS will wage jihad against Britain, before the five men are killed with a bullet to the head.
IS often releases propaganda videos when it suffers setbacks on the battlefield, experts say.
In Iraq last Sunday, federal forces declared victory in the battle for Ramadi, which IS seized in May 2015.
And on December 26, an alliance of Kurdish and Arab fighters in northern Syria seized the strategic Tishreen Dam from IS which the jihadist group had held since 2014.
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IS threatens Britain in new executions video
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IS threatens Britain in new executions video