I left the amp in line, turned off and checked the SWR. The low bands 7 MHz 40 MHz 21 MHz all read high SWR only the 28 MHz showed low SWR; probably just the inherit of the g5rv.
When the amp is off then the antenna relay in the amp bypasses the amp circuit and connects the input directly to the output. The result is that the G5RV is connected directly to the radio and the SWR on the G5RV is what you should see at the radio.
When you have the amp turned on and key the radio then the output of the radio is connected to the input of the amp. The SWR seen by the radio is, at that time, whatever mismatch occurs between the jumper coax and the input circuit of the amp. At that time the output of the amp is connected to the antenna and the amp sees the SWR of the G5RV.
Collins recommends a jumper cable length of 20.5 feet between the radio and the amp input. I assume the length works with the input circuit to provide a reasonable impedance match for the radio.
The other problem is that with no tuner between the amp output and the G5RV the tune and load controls on the amp may not have enough range to match the impedance of the G5RV on all bands.
What I would do is put a 50 Ohm dummy load on the output of the amp in order to eliminate the variable of the G5RV SWR during testing. Use a 20.5 foot length of RG58 between the radio and the amp input. Then see if you can get a reasonable SWR at the radio when you key the amp. and if you can load the amp for full output into the dummy load. If so, then connect the amp to the G5RV and see if you can load it properly for full output on at least some bands. You may need to get a high power tuner in order to provide the amp with a reasonable SWR on some bands.