It should work from the REC jacks; those are the outs. Have you tried the “A” REC out?

Also be sure you’ve used the Browse menu (music notes icon) in the Sonos app to select “Line-In” as your source.

If your turntable has a built-in phono pre-amp, you can connect it directly to the Port by setting the turntable to Line output. It should be set to Phono when plugged into the Sansui (if it has an internal pre-amp, that is — if not it won’t have an output setting).

A far as your SANSUI 5000 is concerned, PORT should be connected to TAPE-A as if PORT is a cassette deck. On the 5000 you should select PHONO. 

Why does it matter which between Tape A and B?

For OP: it appears that the Sansui speaker terminal are not being used? Set the line in on the Port to Autoplay to the desired Sonos speaker, also selecting the toggle for using grouped units.

Some receivers have a feature that allows TAPE 2 to copy TAPE 1 and the user must be more aware of front panel control settings, else PHONO might not be passed through to TAPE 2. 

Fair enough; amps I have known - when they had this feature at all - had just one pair for the loop, and an additional line out that had no corresponding in. This one seems to have two loops.