Soft building blocks, such as micelles, cells or soap bubbles, tend to adopt near-spherical geometry when densely packed together. As a result, their packing structures do not extend beyond those discovered in metallic glasses, quasicrystals and crystals. Here we report the emergence of two Frank-Kasper phases from the self-assembly of five-fold symmetric molecular pentagons. The μ phase, an important intermediate in superalloys, is indexed in soft matter, whereas the ϕ phase exhibits a structure distinct from known Frank-Kasper phases in metallic systems. We find a broad size and shape distribution of self-assembled mesoatoms formed by molecular pentagons while approaching equilibrium that contribute to the unique packing structures. This work provides insight into the manipulation of soft building blocks that deviate from the typical spherical geometry and opens avenues for the fabrication of 'soft alloy' structures that were previously unattainable in metal alloys.