Continuous monitoring of chronic patients improves their quality of life and reduces the economic costs of the sanitary system. However, in order to ensure a good monitoring, high bandwidth and low delay are needed. The 5G technology offers higher bandwidth and lower delays and packets loss than previous technologies. This paper presents an architecture for smart eHealth monitoring of chronic patients. The architecture elements include wearable devices, to take measures from the body, and a smartphone in the patient side and a DataBase with an intelligent system which is able to send an alarm when it detects that it is happening something anomalous. The intelligent system uses machine learning in BigData taken from different hospitals and the data taken from the patient to diagnose and generate alarms. Experiment tests have been done to simulate the traffic from many users to the DataBase in order to evaluate the suitability of 5G in our architecture. When there is low number of users, like 100 or 200 users, we do not find big differences of round trip time between 4G and 5G, but when there are more users, like 1000 users, it increases considerably reaching 4 times more in 4G. The Packet Loss is almost null in 4G until 300 users while in 5G is possible to keep it null until 700 users. Our results point out that in order to have high number of patients continuously monitored, it is necessary to use 5G network because it offers low delays and guarantees the availability of bandwidth for all users.