I also have a 5 year old daughter. Well, she tried all this behavior also. What I do to control it and manage it is if she starts to get worked up over something, I stop her and tell her "Aryana, take a deep breath, then start over" If she's just whining, then I stop her and tell her "don't talk to me with that voice please". It works. They only do what they get away with. If you let them throw the tantrums, they will, if you let them cry over everything, they will, if you let them be rude and disrespectful to you, they absolutely will. Just don't tolerate it. I have two kids, other than my daughter, I have a 4 year old boy. Each of them had ONE tantrum, that's it. I explained to each of them afterwards that that behavior was completely not allowed, and that if they ever did it again, they would be spanked. They never did it again. The day my son threw one we were in Meijer. I was shopping for Christmas toys, and he was sitting on the floor in front of a display of trucks. When I started moving, he refused. He said "No! I want to play!" and I bent down and said "Brayden, I said it's time to go, now stop playing with the truck and let's go." When I started walking away, I heard him behind me...he laid down and started crying. It was completely uncharacteristic of him, had never seen him do that before, but what I did was walk over to him and say "ssshhh, listen to me" and he stopped for a second. I said "When you're finished, you can find me. I said it's time to go, and I'm going." Well, I started walking away with my cart and stopped to "look" at some things a few aisles away (still completely in eye sight). Once he stopped crying, and realized that his tantrum was absolutely having no affect on the situation, he stood up, RAN over to me and held up his arms to me. I basically bent down and explained to him as stated before, said I loved him and gave him a hug.
With my daughter, another thing I make sure I do is explain to her that it's not HER that makes me mad, it's her CHOICES. When she CHOOSES to disobey me, it makes me upset. This seems to work a lot better with children, because their feelings get hurt so terribly, so easily, and it makes them WANT to make better choices also.
If you want anymore tips, let me know, I have a TON of them!!! I do all KINDS of particular things to teach my kids anything from how to handle mean kids at school, to chore and discipline charts, to behavior issues. If something begins to not work, I do some research and find something that does.