If someone is willing to work for $5, they will be willing to work for $15 [0]. The fact that they don't work is at all when the wage floor is $15 is because no one is willing to hire them at that price. Hence, it is a demand side issue.

The supply/demand curve here is a bit tricky, becauce, given a minimum wage of $15, the demand for labor at $14.99 is actually less than the demand for labor at $15, because employers are generally not willing to break the law over $0.01/hr