One sandwich costs 5 times as much as one pie. Iker has just enough money to buy four such sandwiches and eight such pies. However, he only wants to buy pies. What is the greatest number of pies he can buy with $\frac{3}{5}$ of his money?

1. Express the cost of a sandwich in terms of pies

Let the cost of $1$ pie be $1$ unit.
Cost of $1$ sandwich = $5$ units.

2. Calculate the total amount of money Iker has in terms of pie units

Total money = Cost of $4$ sandwiches + Cost of $8$ pies
Total money = $4 \times 5$ units + $8 \times 1$ unit
Total money = $20$ units + $8$ units = $28$ units.

3. Calculate the amount of money Iker wants to spend

Amount to spend = $\frac{3}{5}$ of Total money
Amount to spend = $\frac{3}{5} \times 28$ units = $\frac{84}{5}$ units = $16.8$ units.

4. Determine the greatest number of pies he can buy

Since $1$ pie costs $1$ unit, he can buy $16.8$ pies with this amount.
The greatest whole number of pies he can buy is $16$.