I have no experience sizing and configuring pump systems.
This lies way outside of my area of expertise.
I'm hoping members of this forum can provide some guidance and clarity.
The plan is to install a 5000 gallon vertical tank to store natural rubber latex. The latex will be delivered via bulk tank truck. The need is to pump the latex from the truck to the tank.
The inlet hose length will be 25 feet. The outlet hose length will be approximately the same. The height to the top of the tank is 16 feet. The viscosity of the latex is 6000 centipoise. solids content is 65%.

1. What kind and configuration of pump would be most appropriate for this application?

2. What size drive would be required to power the pump correctly?

3. What RPM's should the pump operate at?

4. What should my inlet and outlet diameters be?

All input would be greatly appreciated.

A PD screw pump might be a good idea, but others will know more than me about that.  In the meantime I suggest you find out something about the flowrate you would need to have from your delivery schedules and from that tank to match your processing activities.  Then we could tell you more about the configuration, size and power you will need for the pump.

Progressive cavity or gear pumps will work and you can use hoses on the suction and discharge side as both type of pumps create very, very low pulsations. But both are rotating PD pumps and 65 % solids is quite a lot. A lot of wear can be expected but on the other side the operating time per year is extremely small.

A peristaltic pump has much less wear but creates pulsations. Therefore solid (plastic or metal) pipes on both ends are much better than hoses. A pulsation dampener will not be needed as the pressure is low and the latex is rather viscous.

A diaphragm pump is the last but most probably the cheapest choice, especially if you have compressed air available. The advantages/disadvantages are the same as for the peristaltic pump. With an AC drive the diaphragm pump will be most likely more expensive. But an air driven diaphragm pump will be cheaper than any other solution. And the energy costs are negligible with less than 20 hours a year.

Suction side inlet size: Not less than 3"
Discharge side outlet: Whatever the pump has
Req. power size (if electrically driven): not less than 0.5 HP (rough estimate)
RPM: Because of the high viscosity I do not recommend more than 50 for a diaphragm or peristaltic pump and not more than 100 for a rotating PD pump. But the pump manufacturers will know that better. 

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