This involves some form of assumptions.

There are 5 more chickens than cows. Chickens have two legs (for a regular chicken) and cows have four legs (for a regular cow).

Assume there are 5 chickens and no cows. There would be a total of 5 x 2 = 10 legs.

Now, the next pair would be 6 chickens and 1 cow. There would be a total of 6 x 2 + 1 x 4 = 16 legs, an increase of 6 legs from the previous situation (because of the extra chicken and cow).

The next pair would be 7 chickens and 2 cows. There would be a total of 7 x 2 + 2 x 4 = 22 legs, an increase of 6 legs from the previous situation (because of the extra chicken and cow).

We continue this process until we get around 17 chickens and 12 cows, for a total of 17 x 2 + 12 x 6 = 106 legs.

There is a non-assumption method using models, but first we assume there are 5 chickens less than stated, so that there are an equal number of chickens and cows.

For every one chicken and one cow, we have 6 legs.

Since the story has it that the total number of legs is 106, having 5 chickens less would mean having 10 legs less, for a total of 96 legs.

Because 1 set (of one chicken and one cow) has 6 legs, there must have been 96 / 6 = 16 sets of animals, so there are 16 chickens and 16 cows in this situation.

In reality, there are 21 chickens and 16 cows for the 106 legs.