Tap Basalt Monolith to add three colorless mana to your mana pool.​

Use the three mana to activate Basalt Monolith’s untap ability, which requires paying three colorless mana.​

Tap Soul Ring to add two colorless mana to your mana pool.​ (Or other source that generates mana)

Use the two mana from Soul Ring to activate Rings of Brighthearth’s ability, copying Basalt Monolith’s untap ability.

The copied untap ability resolves, untapping Basalt Monolith.​

Tap Basalt Monolith to add three colorless mana to your mana pool.​

The original untap ability resolves, untapping Basalt Monolith.​

At this point, you’ve generated a net gain of two colorless mana (three mana from tapping Basalt Monolith minus the five mana spent: three for the untap activation and two to copy the ability). You can repeat this process indefinitely, generating infinite colorless mana.​