Virtually all standalone equalizers deal with analog signals and have physical sliding controls that control a certain frequency band, often 7-15 per channel (mine has 7). At 5.1, this would be 42-90 controls -- it would take up a lot of space and be too fiddly to use. Now your receiver only has speaker level outputs, and virtually every equalizer wants line in-level RCA. So that's just a complete no-go; even if you had 6 RCA outputs you'd still be looking at three separate equalizers (L/R, C/LFE, SL/SR).
The caveat here is that if your receiver is essentially *only* using the multi-channel in, then you can in fact do this with 3 separate equalizers. You'd simply run those 6 inputs into the equalizers, then there would be another...