You need motors that fall within the current range of the drives and also the voltage range. If you have a drive that is 5 amp continuous and 10 peak and a motor that is 5 amp cont and 12 peak then that will be fine but having one that is 7amp cont would cause you problems. You would probably find that the drive would constantly trip on overcurrent, not likely to kill the drive but not likely that it will be much use with the constant tripping. It is obviously best to get motors and drives that are matched. Also even with a matched motor/drive if you are trying to drive an axis that is too heavy for them they will trip but that is just a similar situation to a small stepper trying to drive an axis that is too big.
 Another thing you will need to match up is the feedback, some drives can take resolver feedback, some require encoder feedback and some can take either, same with commutation, some use Hall, some use ABS etc etc.
 I think from the look I had at the Rexroth it depends on the model you have whether it will be any use, you need a drive that will accept Step/Dir signals, some manufaturers call this by different names such as Pulse/Direction, Pulse/Signal etc.
 With the Reliance motors you have you will need DSD-020 or the older DDM-020 or DDM-019. If the motors had been the 240V versions then the current would have been less and a DSD-010 (DDM-010 or DDM-009) would have been enough.

 Not sure what you are doing with the Reliance motors but I am on the lookout for an encoder for an 8 Pole motor of which the Y series motors you have are, so if you decide to get rid of the motors let me know as I may purchase the encoders from you.

Hood

I just register on this Forum, and I think my answer is a little too late, but I'll try anyhow. The Reliance Electric motor's (Y-2012-1-H00AA) part number that you've mentioned is identical to the Allen Bradley's, I have a few Y-2012-2-H00AA which are 220V because of the number "2" on the middle two as follow:

Y        =   Series Designator
#### =   Frame Size  -  12 is the continuous stall torque in Inch/pounds
#     1 =    115V Drive input volts       2 = 230V Drive input voltage
H        =   Incremental encoder (2000 lines/revolution)
00       =    No brake         04  =  24V DC Brake
AA      =   Standard (or Metric)

Your drive won't work because the ####-###-005 are only 2.5 continuous amps. If your motor was a 220V a ####-###-009 would work, since is a 110V you will need at least ####-###-019 Drive.

Luiz