You would need a lot more capacity than you have space for. The rule of thumb is one square foot of bin surface area for each member of the family.

With scraps from six people, you could do both-- have a worm bin and have scraps for an outdoor compost pile too! Do you have a basement? Worm bins are ideal for basements. A worm bin would also allow you to compost year round, unlike an outside compost heap. I guess I'm pro worm bin ;)

With 6 people I would line the 5 gallon with newspaper and fill that. After any large or especially wet addition I would dump the 5 gallon into the outdoor compost and reline with newspaper. The newspaper is to keep the 5 gallon clean and it adds to the compost. I would not wait until the 5 gallon is full to empty. With your space limitations bokashi sounds like it might work well. A few buckets used with only one in the kitchen at a time. Then put this into the outdoor compost bin.

Worm composting can be done in that small space, but I don't think you will achieve the results you are looking for, ie. keeping up with six people. You might try building the 5 bucket worm system, but, again, you will probably get better results from a larger system (or just more of the stacks ;) )