FALSE.
5 pounds of muscle and 5 pounds of fat weigh the same amount: 5 pounds.
The difference is in how much SPACE each of them takes up in your body.
As you can see in the photo, the 5 pounds of fat takes up 2/3 more space in your body than the 5 pounds of muscle does, and that is why you can have two people, both weighing 160 pounds, looking completely different, with one looking slimmer than the other.
The more muscle you have in your body, the leaner/slimmer you will appear, because muscle TAKES UP LESS SPACE than fat, and is also a lot healthier inside your body.
Muscle burns calories 24 hours a day, fat does not.