5. To climb up 7 steps of a staircase, a person can either step up two steps at a time or one step at a time, then there are $\qquad$ ways to climb the stairs.
荅冓 21.
徫析 The problem uses the principle of counting in steps:
First category: 0 times taking 2 steps at once, which means taking 1 step at a time for 7 steps, resulting in only 1 way to climb the stairs;
Second category: 1 time taking 2 steps at once, and 5 times taking 1 step at a time, for a total of 6 steps, with $C_{6}^{1}=6$ methods;
Third category: 2 times taking 2 steps at once, and 3 times taking 1 step at a time, for a total of 5 steps, with $C_{5}^{2}=10$ methods;
Fourth category: 3 times taking 2 steps at once, and 1 time taking 1 step at a time, for a total of 4 steps, with $C_{4}^{3}=4$ methods; In summary, there are a total of 21 ways to climb the stairs.