Let's visit a Zoo!

Probability Level 4

Mrs. Smith the teacher decides to take her class on a trip to the zoo. When they all came at the zoo, Mrs. Smith took 3 children at a time to the lion's cage as often as she can, but she did not take the same 3 children to the lion's cage more than once. After everyone visited the lion's cage, she found that she had gone to the lion's cage 84 times more than a particular child. If the number of children in her class is $N,$ what is the value of $N+5?$

Note: Each child takes as many visits as possible to the lion's cage.