Coronavirus (COVID-19) has adversely harmed the healthcare system and economy throughout the world. COVID-19 has similar symptoms as other chest disorders such as lung cancer (LC), pneumothorax, tuberculosis (TB), and pneumonia, which might mislead the clinical professionals in detecting a new variant of flu called coronavirus. This motivates us to design a model to classify multi-chest infections. A chest x-ray is the most ubiquitous disease diagnosis process in medical practice. As a result, chest x-ray examinations are the primary diagnostic tool for all of these chest infections. For the sake of saving human lives, paramedics and researchers are working tirelessly to establish a precise and reliable method for diagnosing the disease COVID-19 at an early stage. However, COVID-19's medical diagnosis is exceedingly idiosyncratic and varied. A multi-classification method based on the deep learning (DL) model is developed and tested in this work to automatically classify the COVID-19, LC, pneumothorax, TB, and pneumonia from chest x-ray images. COVID-19 and other chest tract disorders are diagnosed using a convolutional neural network (CNN) model called CDC Net that incorporates residual network thoughts and dilated convolution. For this study, we used this model in conjunction with publically available benchmark data to identify these diseases. For the first time, a single deep learning model has been used to diagnose five different chest ailments. In terms of classification accuracy, recall, precision, and f1-score, we compared the proposed model to three CNN-based pre-trained models, such as Vgg-19, ResNet-50, and inception v3. An AUC of 0.9953 was attained by the CDC Net when it came to identifying various chest diseases (with an accuracy of 99.39%, a recall of 98.13%, and a precision of 99.42%). Moreover, CNN-based pre-trained models Vgg-19, ResNet-50, and inception v3 achieved accuracy in classifying multi-chest diseases are 95.61%, 96.15%, and 95.16%, respectively. Using chest x-rays, the proposed model was found to be highly accurate in diagnosing chest diseases. Based on our testing data set, the proposed model shows significant performance as compared to its competitor methods. Statistical analyses of the datasets using McNemar's, and ANOVA tests also showed the robustness of the proposed model.