A cable linkage of some type will be the simplest installation, just needing an anchor bracket, and maybe a bellcrank if the direction of motion needs to ber changed. Don't waste a lot of time and money on designing a mechanical linkage, as you're not likely to be running that setup for very long. You have at least twice the CFM capacity there than the engine can use effectively, so I'm going to predict that it won't be there long. What type of racing are you doing, and how much modification does the rest of the engine have to support that carburetor?
A 250 engine at 5K RPM, with 100% volumetric efficiency (impossible) can only flow 362 CFM. You'd have to be running 7K RPM to use the full capacity of a 500 CFM carburetor. Better do some serious beefing up of the lower end to make it survive at that speed!
Jerry