What does Luke 5:6 mean?

Jesus, a teacher (Luke 5:3) and builder (Mark 6:3) whom John the Baptist called the Messiah (John 1:36), has told Peter to take his boat into deeper water and let down his nets. Although Peter and his partners had fished all night and caught nothing, Peter obeys (Acts 5:4–5). The result is beyond what any of them could have imagined. Peter calls James and John to come out and help. Even so, the weight is too great and both boats are in danger of sinking (Luke 5:7).

Skeptics are tempted to debate if this was a true miracle, implying Jesus merely saw where the fish were biting. The reaction of Peter—the experienced fisherman—gives evidence of a genuine display of Jesus' power and authority over nature. Peter drops to his knees and tells Jesus he is too sinful to be in Jesus' presence (Luke 5:8). Jesus accepts Peter's conclusion but takes authority over Peter's identity. He tells him not to fear and invites him into His ministry (Luke 5:10).

The tense of "breaking" more precisely means they are beginning to break: straining on the verge of snapping. It's interesting that when they reach the shore, Jesus calls James and John while they are mending their nets (Mark 1:19).