Cockpit panel. The solve desk stays visible behind it.

Reduction

Centres, then edge pairing, then solve it as a 3x3 (with parity fixes on even cubes).

Read the overview: 5x5 to 7x7: reduction

1. Centres

First centres

Build the centres in turn.

Last two centres

Commutators for the last centres: 17 cases.

2. Edges

Last two edges

Pair the last edges: 13 cases.