When is it optimal to purchase a Mint on a 5/2 split?
Almost never. A first turn Mint wrecks your economy, and being able to buy good cards on turns 3 and 4 is really important in order to not fall behind your opponent.

Mint/Fool's Gold is an elite opening because it allows you to get a massive density of Fool's Gold in your deck quickly.

Mint/Lighthouse is acceptable, especially if there are lots of attacks, but you need a plan to transition your deck into higher value cards quickly.

Every other opening is sub-optimal, according to the Councilroom statistics (which are derived from Isotropic games).