I think that is fine, especially if you start each exercise later on with a light weight as an additional warm up. I will usually spend the same time for warming up for weight training. For cardio (running) I will just walk slowly to the place where I run, there I will run slowly, and then do sprints before going home. For things like boxing, I will spend at least 30 minutes warming up, as it is really easy to injure the elbows there.