I have won UC cases based on this strategy. However, it may not be entirely necessary. The most relevant factor in your case will be the reason surrounding your final lateness.
Depending on how much money in UC benefits you stand to gain by winning your hearing, it may be worth it to have an attorney represent you at the hearing. If you cannot afford an attorney, many who practice in this area offer reasonably priced consultations.
On a separate note, you may want to speak with an attorney before your hearing to discuss a possible ADA/PHRA claim against your employer if your ADD played a role in your termination. Because your employer will be testifying under oath, UC hearings are a great way of deposing someone before suing them.
My advice: contact an attorney on this thread.
9 is a large number. I think specifics would need to be known. The records will be important. I do not know how late you were on those occasions, but that can be a factor. What was the span of time involving the last 5 that you feel were the reason for the termination.
This is not intended as individual legal advice and there is no attorney client relationship established by this answer. It is advisable that you seek individualized legal assistance. This is not a substitute for hiring an attorney.
To add to Mr. Auerbach's response, you may also have a FMLA claim, in the event your employer is large enough to be subject to the FMLA. You should consult with an employment attorney; many will offer a no-cost consultation.
Answers to questions on this forum do not create an attorney-client relationship.