The short answer
In feng shui, 5 is generally treated as neutral. It is not usually described as lucky or unlucky in itself. It stands for the centre and for the five elements, which are wood, fire, earth, metal and water. Its meaning depends on the setting, and it is most often discussed in the context of the Lo Shu square and the Flying Stars system.
The five elements and the centre
The five elements are wood, fire, earth, metal and water. They work together in a cycle. In that cycle, 5 represents the stabilising centre that connects the other elements. Many practitioners describe it as a balancing number rather than a lucky or unlucky one.
The Lo Shu square
On the Lo Shu square, 5 sits in the centre. The centre, which the bagua map treats as the health area or tai chi, is linked with the earth element and with the overall harmony of the household. Because it is the centre, the number 5 is not assigned to one of the eight compass directions the way the other numbers are.
Yellow 5 in Flying Stars
The Flying Stars system is a different method from the kua system. In that system, the Yellow 5 star is traditionally seen as a challenging star. Practitioners often describe it as a star of obstruction or misfortune, and some use metal objects, such as five-rod metal wind chimes, as a traditional way to reduce its effect. This is a specialist idea, and it is separate from the kua number.
Five in the kua system
The kua system has no kua 5. If your calculation gives 5, men become kua 2 and women become kua 8. The kua number guide explains the full calculation and the rule for 5.
Five in everyday numbers
People ask about 5 in house numbers and phone numbers as well. In those cases, the answer is the same: 5 is generally neutral in feng shui. A house number does not change your kua number, and the house numbers guide explains the difference.
For the system that gives each person their directions, see the Eight Mansions overview.
These are traditional ideas, not scientific findings. Use them as a way to think about a number, not as a rule for a decision.