Prozac Insomnia

I am on day 10 of Prozac and my only major side effect is insomnia. I can fall asleep fine, but staying asleep is an entirely different story. I sleep for a solid 5 hours at most, then I have trouble going back to sleep. Has anyone else experienced this and does it go away? Also, I take melatonin every night, because I was afraid of this happening and the result is five hours at a time.