Silicon surface alloys and silicide nanolayers are highly important as contact materials in integrated circuit devices. Here we demonstrate that the submonolayer Si/Ag(001) surface reconstruction, reported to exhibit interesting topological properties, comprises a quasi-one-dimensional Si-Ag surface alloy based on chains of planar double-pentagon Si moieties. This geometry is determined using a combination of density functional theory calculations, scanning tunnelling microscopy, and grazing incidence x-ray diffraction simulations, and yields an electronic structure in excellent agreement with photoemission measurements. This work provides further evidence of pentagonal geometries in 2D materials and heterostructures and elucidates the importance of surface alloying in stabilizing their formation.