For a long time sleep was not considered a basic human need. Studies on sleep deprivation helped to change this in the 20th century. In terms of human need, sleep is one of the five most important elements. Sleep deprivation can cause a myriad of problems ranging from decreased body temperature to cognitive impairment and hallucination.
Although the mechanisms of sleep are not well understood, the problems associated with lack of sleep are. Headaches can begin as soon as 24 hours after missing sleep. 72 hours in, memory is impaired and temporal and spatial distortion start to occur. After 96 hours without sleep, cognition is markedly impaired. After 144 hours, hallucinations ensue and there is a considerable loss of attention and manual dexterity.
The longer a person goes without sleep the less coherent thought patterns become. This lack of clear thinking can be detrimental on its own, if coupled with a lacking in any of the other basic needs areas it could be life threatening.
There are other things you could add to this list like sex, emotional connection, sense of belonging, etc. The difference is that although sex is needed for the species to survive an individual can live without it. Emotional connection and a sense of belonging are group needs, not individual survival needs. The truth is, there are only five basic needs; Clean Air, Water, Nutrients, Shelter and Sleep.
Beyond our health, the simple fact is that our entire society is based primarily on the existence and leveraging of these five factors. They are the basis for concepts like family, wealth, health and, at times, governments. Without air, water, food, sleep or shelter, none of us would see it past our first few days on Earth.