B.,
Wow. 5 and 15. That's quite a stretch.
Here's three discipline concepts to think about: boundries, consistancy, and logical consequences.
Boundries
When kids don't have a clear idea of what behavior is ok and what is off-limits, they push you around, sometimes just to see if you notice that they are there!. I don't mean only what you tell them, I mean what you let them do without any real consequense.
For example: you tell your 5 not to whine, but after 10 minutes of whining you get that candy at the check out. So 5 knows whining is ok, it gets me what I want.
Another example: You tell 15 that homework needs to get done every day. But you don't have any guidlines about WHEN homework needs to be done, so she ends up not doing it because its too late, or something else came up etc.
Consistancy
Once you figure out what boundries you want to set, consitancy is the issue that will make or break the whole game. You gotta stick to your guns here. If you get pushback, especially from the 15, you have to help her find a way to stay within the boundries (since you have band that afternoon, you'll have to miss that tv show to do your schoolwork. Maybe we can record it for later.) If whining is an issue, Be Consistant.
Logical Consequences. You want to give the kids a reason to change their behavior and attitudes. If 5 is yelling and throwing a temper fit, then she is not fit for the company of others and must go to her room. She can come back when she is ready to apologize and be civil. I'm not sure what 15's issues are, but connect the behavior you don't like to a 't want to related consequence that 15 dosen't want to happen (for example, When you don't help around the house at least 20 min a day, I won't drive you to your extracirricular activities)