Deborah Arin at Stepping Stones is excellent. She is in Healthcare City. She may have a waiting list but she aslo has two other Speech Therapists working with her who I've heard are very good also.
Kalimati Speech & Communication Centre in Mirdif is new and I've heard good things about it. As they are new their waiting list might not be too long:)
I would also recommend Rashid Paediatric Therapy Centre, KidsFirst, Dubai Community Health Centre for good speech therapists, but I don't know what the waiting lists are like for each one. I am a therapist at one of these establishments and so know where is reliable and professional!! You can google for each one.
City Hospital have a good speech therapy department, sure helped me when I had problems last year following surgery and got me speaking agin. Room is set up for children and have lots of toys, soft mats etc and the therapists are very nice.
For a 5 and a half year old? My child has quite a severe open bite (not over bite) from thumb sucking. The pediatric othordontist has advised speech therapy while we wait for the permanent teeth to come in before orthodontic intervention. He obviously can't make any of the sounds that requires closing the front teeth together and people who don't know him say he is quite difficult to understand.
Thanks