5. Divide eleven cakes equally among six girls without cutting any cake into six equal pieces.
5. Out of 11 cakes, we give each girl one, then we will have 5 cakes left $-11: 6=1$ (remainder 5). We will divide each of the 5 cakes into two equal halves. We will get a total of 10 pieces. They can be divided equally among 6 girls as follows: 10:6 = 1 (remainder 4). Thus, each girl will get one more half of a cake.

Then we will divide each of the remaining 4 halves into two parts. The eight quarters obtained will be divided among 6 girls $-8: 6=1$ (remainder 2). Each of them will get one more quarter. We will divide each of the two remaining parts into three parts, so everyone will get an equal share. Finally, we get: $1+1 / 2+1 / 4+1 / 12$.

Answer: $1+1 / 2+1 / 4+1 / 12$.