One last idea:

Since you still need to do the parity confirmation after the buffer is filled with 40, five bit bytes... there are some reasonable combinatorial shortcuts in doing that.

I'd bet you could test all forty bytes at once by simply xoring each byte in sequence with the accumulator. An adjustment would need to be made to the accumulator at the end to test the 2 parity bits against the 4bit parity run.
This technique is statistically susceptible to pairs of parity error and a matching reversing parity error that would go undetected. However, since we'r running through a data buffer of 40 bytes, the probabilities would be much rarer than most would initially imagine.

Before implementing this technique, it should be mathmatically proven with an excel spreadsheet. But you could still decide to parity match each 5 bit byte through the 40 byte buffer in reasonable speed and be 100% sure of validation.

That was a fun puzzle!

-Jay C. Box