Well looks like you have a pretty good start.
Basically what you're asking the judge to do is to withhold adjudication on one of your prior moving violations. Explain a letter that you have a five year license revocation and what your driving needs are- you may want to further indicate to the judge that you are willing to pay a higher fine or take a driving school to achieve your goal.
In order to have one ticket "dismissed", it may depend on how long ago the ticket was. Basically, you would have to file a motion to vacate or set aside the conviction (for the other driving while license suspended). Which ticket you ask to set aside may make a difference. It would be a good idea to speak to an attorney about the process, your options, and the likelihood of getting it done. Also, please realize you only have to wait 1 year of the 5 year suspension to be eligible for a hardship license (which it seems you have great reasons for). I am not sure what stage you are in, but I have had many clients come to me half way into their 5 year suspension after getting a new DWLS charge, and they never were told they could have gotten a hardship long before. One way or another, you should definitely find a way to get a permit or avoid driving, because if you are again charged with driving while your license is suspended after already being habitualized, you may no longer qualify for a hardship license. Also, a hardship license isn't just for work. They allow you to do anything you need "to maintain your livelihood", which can be very broadly interpreted. Feel free to contact our office or a local attorney who does this type of work to go over your rights and options.