Does this fit the vitamix 5000?

Not sure. I have a 7500. Vitamix literature suggests that it probably will fit. I would ask them directly though.

Will the 32oz container work on the professional 750 - since it does not have the same 'square' base?

Yes, I have the combo and it works (it fits inside the rubber feet on the machine instead of outside)

which tamper tool fits the 32 oz container?

Order the mini-tamper from Vitamix.com. Amazon does not sell the mini-tamper. I have noticed that some people recommend using the longer tamper that comes with the tall 64 oz. container, because that particular tamper has a step that in theory will prevent it from reaching the blades in the shorter 32 oz. container. Unfortunately, there have been too many instances of that tamper being pushed vigorously enough to cause it to go past the step and hit the blades of the 32 oz. container, which destroys the end of the tamper. It's not worth the risk... just get the correct tamper for the job, the mini-tamper.

Item Dimensions D x W x H	17.8D x 17.8W x 33H centimetres
Item Weight	1.36 kg
Capacity	64 Fluid Ounces
Voltage	110 Volts
Power Source	Corded Electric
Wattage	200 watts
Special Features	Blends
Style Name	Countertop Blenders
Colour	Transparent
Is the item dishwasher safe?	No
Blade Material	Stainless Steel
Material Type Free	BPA Free
Material Type	BPA-free Eastman Tritan Copolyester

Vitamix 015856 Classic 15856 Container, 64-Ounce, Clear, BPA-Free Eastman Tritan Copolyester

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