Question 1146445
Since there are no cards left over when 5 or 7 people are playing, that means the number of cards is divisible by 5 and 7.  
5 * 7 = 35
35/2 = 17 r 1
35/3 = 11 r 2
35/4 = 8 r 3
35/6 = 5 r 5

Therefore, 35 is the minimum number of cards possible.