  We elaborate on a recently found SU(5) relation confined to the up-(s)quark
flavour space, that remains immune to large quantum corrections up to the TeV
scale. We investigate the possibilities opened by this new window on the GUT
scale in order to find TeV-scale SU(5) tests realizable at the LHC. These SU(5)
tests appear as relations among observables involving either flavour violation
or chirality flip in the up-(s)quark sector. The power of these tests is
systematically evaluated using a frequentist, p-value based criterion. SU(5)
tests in the Heavy supersymmetry (SUSY), Natural supersymmetry and Top-charm
supersymmetry spectra are investigated. The latter scenario features light
stops and scharms and is well-motivated from various five-dimensional
constructions. A variety of SU(5) tests is obtained, involving techniques of
top polarimetry, charm-tagging, or Higgs detection from SUSY cascade decays. We
find that O(10) to O(100) events are needed to obtain 50% of relative precision
at 3-sigma significance for all of these tests. In addition, we propose a set
of precision measurements in ultraperipheral collisions in order to search for
the flavour-changing dipole operators of Heavy supersymmetry.
