The camera really does add 5kg. Here's a good look at the effect that different lenses and barrel distortion can have when it comes to making you look fat on camera. The gif from Jim Zub starts by showing a person's face with a 20mm lens and then goes all the way up to 200mm. You basically watch his face and hair expand right before your very eyes.
When they say
"The camera adds 10 pounds"
they're not kidding.
Here's the effect with different camera lenses: pic.twitter.com/xmwbsflVKd
— Jim Zub (@JimZub) July 26, 2016
Here's another image detailing the "camera adds 5kg" effect:
There's a combination of factors that make you look fat. The focal length of the camera can flatten out a person's features thus making them look much bigger in comparison. Barrel distortion — that is, when straight lines look like they're curving out because of the nature of the lens — can also make a person's face look more plump than usual.
Basically, never take a picture of yourself.