I have a 5 year old child. no custody has been established with me nor her mother . I would like to file for primary custody.

I know this sounds unhelpful, but with the facts you've set forth you should hire an experienced family law attorney. It sounds like you have some legitimate concerns, but you have to avoid making this all a financial issue. Being poor and being a poor parent are two different things. Tread lightly there.

Also, it's not fair, but men often have a harder time getting custody. Take a parenting class to show the court that you're serious about being a good parent.

You should consult with an attorney who is experienced in child custody matters, for more information that is specific to your case and jurisdiction. In general the issue in a custody case is what is in the best interest of the child. That doesn't mean who can best afford to care for him but where is he better off. Stablilty, finances, emotional health, living situation are all issues that the court would consider in making its decision. You will however need to be able to submit proof that shows that your circumstances would be better for your child and that disrupting him from the relationship he has had with his mother would be outweighed by the benefit of residing with you. Based on what you say her reaction was to offering to take your son more, you better be ready for a battle back from her. If you have any baggage of your own, please tell your attorney, so that your attorney can be ready to address it if it comes up, as it is likely to. An attorney can only truly assess your liklihood of success if he/she knows all of the facts, not just the information on the child's mother.
Oh and make a copy of the bashing on the myspace and don't do things like that back. Be prepared to accept an expansion of your visitation in lieu of full custody, sometimes baby steps get you what you want down the road. Good luck.