While the United States of America does not have exit immigration check, if you leave by air or by land into Canada (there is no control on entering into Mexico by land and even Mexico authorities keep no records), the CBP will know who left and when from data provided by the airlines (and by Canadian immigration department). It is not perfect but has gotten much better in recent years. Thus, it is tempting to overstay because there are stories that people keep telling about how they were never caught even though they 'live' and 'work' in USA on a tourist visa. However, many of those who overstay are starting to realize that they have been turned back at the airport or ordered to leave within a certain period of time (normally 72 hours). Typically, they confiscate your passport, and make a notation in your passport cancelling your visa and banning you typically for five years.
So would it not be great if you could simply apply for a new tourist visa? Hell, no. When the 5-year ban was put in place, the agency made sure that the information about you is in the system and the embassies all over the world will have access to that information. It would not matter if you renewed your passport in the meantime, because in any case, when you show up at the airport, your fingerprints will be in the system. So the right thing to do is to just wait for five years and then apply. Chances are very high that you will be denied again, particularly if you have family here and the consulate suspects that this time you will simply never leave.