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We present the results of an extensive exploration of the five-dimensional parameter space of the minimal SU (5) supergravity model, including the constraints of a long enough proton lifetime (τ p > 1 × 10 32 y) and a small enough neutralino cosmological relic density(Ω χ h 2 0 ≤ 1). We find that the combined effect of these two constraints is quite severe, although still leaving a small region of parameter space with mg < ∼ 90 (110) GeV for α 3 = 0.113 (0.120). Thus, if this model is correct, at least one of these particles will likely be observed at LEPII.