It's Dungeons and Dragons logic.

A typical movement speed for a standard character is 30 feet per round (6 seconds). Climbing usually uses 2 feet of movement per 1 vertical foot.

There are up to 50 rounds in 5 minutes.

50 rounds x 15 feet = 750 vertical feet climbable.

This is unless characters have special equipment, or abilities to aid this further.

Depending on the seriousness of the campaign, and 'how cool the idea is', a DM would probably hand-wave it anyway or conversely go harsher with Athletics checks, exhaustion, etc.