The cloud market is characterized by fierce rivalry among cloud service providers. The availability of various services with identical functionalities on the market complicates the selection decision for service requesters. Although objective trust measurements can be used to evaluate the trustworthiness of services, they are not always available and are static in nature. Subjective approaches are not always viable because they often require repeated service invocations to collect client feedback. To overcome these limitations, we propose, in this paper, a reputation-based trust assessment approach that combines the Net Brand Reputation (NBR) measure with a deep learning-based sentiment analysis model using online user reviews. CBiLSTM is the name of the proposed deep learning model that hybridizes the Convolutional Neural Networks (CNN) and the Bidirectional Long Short-Term Memory (BiLSTM) layers. The CNN layers deal with text inputs' high dimensionality, while the BiLSTM layer explores the context of the extracted features in both forward and backward directions. CBiLSTM was trained on a new dataset named CLOSER-DREAM, containing more than 13,000 reviews relating to several emerging cloud services to classify these reviews and assess the overall reputation of the cloud services providers. The results of the series of experiments that were conducted have shown that CBiLSTM outperforms the classic deep learning models with 98% of precision, 99% of recall, 98% as an F1-score, and 99.7% of accuracy. Also, CBiLSTM offered a reasonable training time of about 519ms with the CLOSER-DREAM dataset. The classification obtained by applying CBiLSTM was proven to be an effective method to calculate the NBR measure used for the reputation assessment of cloud service providers. The proposed technique yielded an NBR score of 98.3% for Google cloud services, which is close to the real/actual NBR of 96.25%.