Four were treated for smoke inhalation and one was taken to hospital with burns, Devon and Somerset Fire and Rescue Service said.
The gorse fire, which began at about 13:45 BST, has engulfed a large area of dry heath-land on Woodbury Common.
Twenty fire engine crews were sent to tackle the flames that were fanned by high winds.
The fire is being fought on a number of fronts and a police helicopter has been deployed to help survey the scene.
Chief Fire Officer Lee Howell said it was a "very difficult incident" and his teams were struggling with wind direction and a lack of water supplies.
He said: "It's a very, very large area - at the moment it's difficult to quantify and there is a fire front on a number of different parts of the common - and so our resources are being targeted to bring that under control in a number of different areas."
He added that firefighters will be at the scene overnight and into the early hours of Monday morning.
The nearby Woodbury Park Golf and Country Club has been evacuated as a precaution.
Smoke can be seen for miles around and the public have been advised to avoid the area.

The Reds, who are fifth in National Two South, beat third-placed Chinnor 29-12 for a second win in a row.
"Tommy Phillips, Ben Priddey and Craig Williams really led the team from the front," Churcher told BBC Cornwall.
"If your front row and front five are making 70-plus tackles in a game you're going to be doing well and that's what happened against Chinnor."
The Reds face seven teams who are below them in the table in their next eight games, as well as league leaders Old Elthamians.
Churcher believes his side still has a lot of room for improvement, adding: "Chinnor wasn't the complete performance, but emotionally it was a really dogged performance.
"We've got to build on what we did last weekend, because if we don't, last weekend will have been a waste of time."

Driver Henry McPherson, 61, from St Fergus, died after the accident on the A952 near Mintlaw in 2014.
Pauline Flynn, 36, denies causing death by careless driving.
Mr McPherson's partner Patricia McPherson, 52, told Peterhead Sheriff Court she remembered the look of fear on his face.
Ms Flynn, of Mintlaw, allegedly crossed on to the opposite side of the carriageway while driving along the Clola to Toll of Birness road.
Mrs McPherson said: "I became aware that I was to be in a crash when I saw lights cross from the other carriageway lighting up the central line, the driving line of the road.
"The lights were right in my face.
"The next thing I remember after that is a feeling like I was in a washing machine.
"It was a bit surreal. I felt like I was in a washing machine going round and round and can remember hearing myself screaming.
"And I can remember looking over at Harry and he had a look of fear on his face that I had never seen in my life."
Mrs McPherson described Mr McPerson as a masculine man who would not have shown anyone when he was scared.
She went on: "I think he knew it wasn't going to end well."
Mrs McPherson said her partner of 34 years, who was known as Harry, had his arms stretched straight out in front on him on the steering wheel.
She said she then felt as if she was being crushed from the front of her chest to her back and could  barely breathe.
Mrs McPherson said: "I can remember being in the car and feeling crushed and I can remember a strange smell of earth or soil.
"I couldn't understand why I was smelling earth. I didn't at that stage realise the situation I was in.
"I didn't realise I was in a crash."
Defence lawyer Susan Duffy asked Mrs McPherson if she wanted someone to be responsible for the death of Mr McPherson and her subsequent fracture injuries.
She replied: "I don't want anyone to be responsible for that no. I want to have my partner back."
The trial continues.
Five firefighters have been injured while tackling a blaze on common land near Exeter.
[NEXT_CONCEPT]
Redruth boss Marek Churcher says his side's front row have been key to the club's good form.
[NEXT_CONCEPT]
A woman whose partner died after a car crash in Aberdeenshire has told a trial she felt as if she was "in a washing machine" after the collision.