As stated above, going from 4-20 mA to 1-5 VDC over a 250 Ohm resistor works fine - I've done it many times.
Don't try it the other way from 1-5 VDC to 4-20 mA. The math works out, of course, but most voltage output transmitters have a very high minimum impedence - usually in mega-Ohms. It looks like yours requires at least 1 k-Ohm. Putting the 1-5 VDC over a small resistor looks like a short circuit to the transmitter, and it will draw more current than they can put out. At the least the transmitter will drop out, at the most the smoke will escape from the transmitter.
Use a signal conditioner. AutomationDirect.com, Acromag, Action Instruments, APi, and many many others build these.