The Compact RIO can be part of your system, it is not the solution. You will require additional modules to the base of this Compact RIO module.
Keeping aside what your CompactRIO system is currently being used for, I would suggest that you downconvert your RF to a suitable IF and then use appropriate ADC for sampling the IF. There are good number of IF sampling ADCs from many vendors like Analog, TI, etc. so you can choose a particular chip/set from the ones available. FPGA will come into picture where you have your fixed signal processing tasks ported to VHDL from your preliminary studies.
Again your bandwidth is 160MHz so you will also have to work your RF/IF front-end circuit before the ADC.
I think the alternative way is to apply acoustooptical cell for processing of 160MHz signal at frequency of 5/8 GHz. But, I am not sure if it is possible to buy such AO cell on the market. Of course it must be specially designed for you by your order.