Try:
uA[r_, phi_] := BesselJ[3/2 r, 5]*Exp[I 5 phi]; TransformedField["Polar" -> "Cartesian", uA[r, phi], {r, phi} -> {x, y}] (*E^(5 I ArcTan[x, y]) BesselJ[3/2 Sqrt[x^2 + y^2], 5]*)
