Three weeks is 7*3=<<7*3=21>>21 days.
She traveled one day to her grandparents' house, one day to her brother's house, two days to her sister's house, and two days back home for a total of 1+1+2+2=<<1+1+2+2=6>>6 days.
She spent 5 days at her grandparents' house and 5 days at her brother's house, for a total of 5+5=<<5+5=10>>10 days.
Thus, of the 21 vacation days, the number of days remaining to spend with her sister was 21-6-10=<<21-6-10=5>>5 days.
#### 5