Where does the chart require you to be at 5000' over LZR? The transition from LZR has a bearing of 154, distance of 2.4 and minimum altitude of 3300' (it's not well indicated but there is a transition from LZR, it's just not indicated in the profile view). With an MSA of 3500', once cleared for the approach and within 25 sm, you may descend to the MSA. At the IAF (LZR), you go to 3300'. At 12.5D, continue your descent to 2800. It's the 2800' at the FAF that leaves you high and which is probably why there are no straight-in minimums.
Now as far as an arrival dumping you over LZR at 5000', you may not make the 12.5 fix at 3300', but if you're reasonably ahead of the aircraft, you should be able to make the FAF at 2800'. It might be tight in a big aircraft in which case, I would request clearence to LTE, do the course reversal and the full teardrop procedure.
I agree with Bookworm, if on the arrival, unless specifically cleared to LZR for the approach, stay at 5000'. If you're slow and configured, 1700' in 2.4 nm is doable. I'm not sure what RNP, B-RNAV or WGS-84 has to do with the altitudes you could fly on the approach.