How huge is huge? The rest of the chain sounds pretty straightforward, even at 5MHz. That's not to say that an FPGA is wrong for the application, but nothing in that list screams "must use FPGA" to me.
However, the whole program screams "get to market, then iterate" to me, which is a very effective way to move forward with a product like that.
Note: I've shipped products doing continuous signal processing on DSP, GPU, CPU, SoC, and FPGA. (MCU eventually... Give me time.) I did the mental swag on the described processing chain...
Out of curiosity, how big is your FPGA?