We consider a class of well motivated string-inspired flipped SU(5) supergravity models which include four supersymmetry breaking scenarios: no-scale, strict noscale, dilaton, and special dilaton, such that only three parameters are needed to describe all new phenomena (m t , tan β, mg). We show that the LEP precise measurements of the electroweak parameters in the form of the ǫ 1 variable, and the CLEOII allowed range for B(b → sγ) are at present the most important experimental constraints on this class of models. For m t > ∼ 155 (165) GeV, the ǫ 1 constraint (at 90(95)%CL) requires the presence of light charginos (m χ ± 1 < ∼ 50 − 100 GeV depending on m t ). Since all sparticle masses are proportional to mg, m χ ± 1 < ∼ 100 GeV implies: (155) GeV, and mν < ∼ 100 (140) GeV in the no-scale (dilaton) flipped SU(5) supergravity model. The B(b → sγ) constraint excludes a significant fraction of the otherwise allowed region in the (m χ ± 1 , tan β) plane (irrespective of the magnitude of the chargino mass), while future experimental improvements will result in decisive tests of these models. In light of the ǫ 1 constraint, we conclude that the outlook for chargino and selectron detection at LEPII and at HERA is quite favorable in this class of models.