1. Define the likelihood that an individual will contract a specific disease
Supervised learning. The outcome is defined as the binary classification of testing positive or negative for the specific disease.

2. Translate a set of images into variables for modeling
Unsupervised learning. The type and number of variables in the set is not know in advance, so an unsupervised learning algorithm is needed to tease out useful features.

3. An ecommerce company wants to identify power users
Supervised learning. 'Power users' will have a certain set of defined attributes, such as time & dollars spent on the site.

4. That same company wants to see shopping patterns in users
Unsupervised learning is useful for identifying patterns.

5. You want to reduce the number of variables inputting into your random forest model
Unsupervised learning. This requires exploring the data to discover relationships among the variables, such as interfeature correlations.