Dynamic conductance between a normal-metal (N) Au tip and the heavy-fermion superconductor (HFS) CeCoIn5 single crystal has been measured. The contact is shown to be in the Sharvin limit. Our clean conductance spectra are reproducibly obtained over a wide range of temperature (60 K to 400 mK). The background conductance shows a gradual development of asymmetry, starting at T* (∼ 45 K) down to Tc (2.3 K), which we attribute to the emergence of the heavy-fermion liquid. The enhanced sub-gap conductance observed below Tc, arising from Andreev reflection (AR), is an order of magnitude smaller (∼ 13.3% at 400 mK) than that observed for N/conventional superconductors but consistent with other N/HFS data reported. From analyses using an extended Blonder-Tinkham-Klapwijk model, we find the conductance data at 400 mK is consistent with strong coupling (2Δ/kBT c = 4.64), and that the temperature dependence of the zero bias conductance is consistent with a d-wave order parameter, in agreement with the literature. However, attempts to fit full conductance curves as a function of temperature clearly show that this model cannot account for our data. We provide restrictions and suggestions for theoretical studies to account for AR at the N/HFS interface.