As per Gauss Theorem,
E = σ/2ɛ.
where σ is surface charge density and ɛ. is the permittivity of free space.
e is charge on electron and r. is min. distance of approach.
Surface potential energy of charged plate = KE of electon
qe = e x σ/2ɛ. x 5 x 10-3m
10-3 = σ/2ɛ. x 5 x 10-3
σ = 2/5 ɛ.