Is an image with 5 labels equivalent to 5 images with 1 label?
No. These are two separate problems. Multi-label classification and multi-class classification. In general, when we talk about classification we mean multi-class classification i.e. there are a certain number of categories and the input training samples fall into only one of these which is your case of 5 images with 1 label. In the case of 1 image with 5 labels, it is a multi-label classification, which is a generalization of multi-class classification. Both of these are different tasks and the use case depends on the problem that you are trying to solve!