Digital filter implementation in C (embedded)
No, if you feed in a signal containing frequencies to 16 kHz, your filter will need to sample at at least 2*16 kHz for all bands. If you sample only at 160 kHz, you'll have to design each filter for that sampling rate. 

You could use a lower sampling rate for the lower frequency filters, while keeping the sampling rate above the highest frequency present (16 kHz ?). Thus, taking every 2nd sample and using the 16 kHz (160 kHz sampling) would work for 8 kHz -- but conflicts with the rationale for choosing 5x oversampling in the 1st place (that's not strictly necessary -- it depends on the highest frequency components in the signal). 

Note that if you extended this thought to the 31.5 Hz band, you'd use every 500th sample == 160k/500 = 320 Hz, which wouldn't work with the whole signal since it contains components to (and beyond ?) 16 kHz.