There are no specific rules for drowning in DnD 5e; however, there are rules for suffocating, which can be used for drowning. A creature can hold its breath for (1 + Constitution modifier) minutes (minimum 30 seconds).

When a creature runs out of breath, it survives (Constitution modifier) rounds (minimum 1). At the start of its next turn, it drops to 0 hit points and starts dying (making death saving throws).

For example, a creature with 16 Constitution (+3 modifier) can hold its breath for 4 minutes. After that, it survives for 3 rounds (18 seconds). On the 4th round, it falls to 0 hit points and is dying.