Answer: $2 ; 3 ; 4$.

Cashback is the percentage of the purchase amount that is returned to the card after the purchase.

Let's calculate the cashback that Petya will receive in each case:

1) $2000 * 0.05 = 100$ rubles;
2) $5000 * 0.03 = 150$ rubles;
3) $3000 * 0.04 = 120$ rubles;
4) $3000 * 0.05 = 150$ rubles;
5) $1500 * 0.06 = 90$ rubles.
2. Petya is the owner of a cashback card offering 1% on all purchases. In addition to this, the bank offers Petya the option to choose categories with increased cashback each month, but no more than three. Which categories would be the most profitable to choose, considering the cashback percentage and the expected expenses?
1) transport: cashback - 5%, expenses - 2000 rubles
2) groceries: cashback - 3%, expenses - 5000 rubles
3) clothing: cashback - 4%, expenses - 3000 rubles
4) entertainment: cashback - 5%, expenses - 3000 rubles
5) sports goods: cashback - 6%, expenses - 1500 rubles