This paper presents the methods we developed for the Nuanced Arabic Dialect Identification (NADI) 2023 shared task, specifically targeting the two subtasks focussed on sentence-level machine translation (MT) of text written in any of four Arabic dialects (Egyptian, Emirati, Jordanian and Palestinian) to Modern Standard Arabic (MSA). Our team, UniManc, employed models based on T5: multilingual T5 (mT5), multi-task fine-tuned mT5 (mT0) and AraT5. These models were trained based on two configurations: joint model training for all regional dialects (J-R) and independent model training for every regional dialect (I-R). Based on the results of the official NADI 2023 evaluation, our I-R AraT5 model obtained an overall BLEU score of 14.76, ranking first in the Closed Dialect-to-MSA MT subtask. Moreover, in the Open Dialect-to-MSA MT subtask, our J-R AraT5 model also ranked first, obtaining an overall BLEU score of 21.10.