Generally, the answer to your question is yes. Most prosecutors and judges will work with you to help you avoid the five year suspension. It is very important that you have a valid license when you conduct the plea negotiations. I strongly advise you to retain a lawyer to handle these negotiations for you.
This is definitely a possibility. As you noted, three "big" driving charges in five years (i.e. three DWLSRs in five years) will cause you to be labeled as a Habitual Traffic Offender (HTO) and have your license suspended for five years. Pleading to a No Valid Drivers' License charge will keep you from being labeled a HTO by the Department of Highway Safety and Motor Vehicles. Being able to show a valid drivers' license will go a long way towards convincing the State to amend the charge to No Valid Drivers' License.
I agree with both of the prior writers. I have, on numerous ocassions, successfully negotiated with the State Attorney's Office to have a client's DWLSR charge amended to a No Valid DL. As the other attorneys stated, it is best to have an attorney negotiate this for you. The consequences of not taking care of this properly are severe. You will not only be labeled a Habitual Traffic Offender (HTO), but any future driving charge that you pick up MAY be charged as a felony. It would be very wise to nip this issue in the bud, do what you have to do to get a valid DL, and move on.
I have a very good friend in Orlando that can handle these types of cases, If you would like his information, please contact my office.