The ability to operate transmitters and receivers at the same site depends on several factors.
The frequency separation
The filtering on the input circuits of the receiver
The linearity of the RF amplifier and mixer in the receiver
The screening of the receiver and transmitter circuits
The phase noise spectrum of the transmitter.
How these factors apply in your situation:
Frequency separation, 900Mhz and 5.8Ghz are widely separated and not harmonically related. This is good.
Filtering, Linearity, Screening, and Phase Noise are completely unknown at the moment.
My only suggestion would be to set it up and see what happens, my best guess is that it will work fine if you just separate the 900Mhz and 5.8Ghz antennas as much as possible in your situation.
You also infer full duplex operation on 900Mhz, this will certainly be problematic.
To do this you will need a wide as possible frequency separation between transmit and receive.
As mentioned by mneary, it is quite common practice in amateur radio repeater operations to operate transmit and receive simultaneously on a single antenna at both VHF and UHF frequencies.
However the frequency separation is of the order of 0.4% and the filtering requirements for the diplexer and transmitters and receivers is severe.
Do you really need simultaneous transmit and receive at 900Mhz, or is rapid changeover half duplex good enough?
JimB