||We study the infrared physics of 5d N = 1 Yang-Mills theories compactified on S-1, with a view toward 4d and 5d limits. Global structures of the simplest Coulombic moduli spaces are outlined, with an emphasis on how multiple planar 4d Seiberg-Witten geometries are embedded in the cigar geometry of a single 5d theory on S-1. The Coulomb phase boundaries in the decompactification limit are given particular attention and related to how the wall-crossings by 5d BPS particles turn off. On the other hand, the elliptic genera of magnetic BPS strings do wall-cross and retain the memory of 4d wall-crossings, which we review with the example of dP(2) theory. Along the way, we also offer a general field theory proof of the odd shift of electric charge on Sp(k)(pi) instanton solitons, previously observed via geometric engineering for low-rank supersymmetric theories.