1, 2, 3 and 5 not a proper language, language error. proper language: Which one do you think is the best? 4 still can be accepted, but suggest you put in this way: In your opinion, which one is the best?

#1- is technically correct but sounds more British English than anything; in the USA we'd add the word "is" ("Which one do you think is the best?"). #2- This can also be used but is less proper/correct. #3- is wrong :) #4- This is good and is a little more elaborative; perhaps a bit more formal but also more "educated". #5- This one's order is a little mixed up (if you want proper/correct); "Which one do you think is the best (one)?"; almost what you had for #3. -The 2nd "one" in #5 is optional. Hope this helps! ^_^ Le meas, ~_~. Maidhc

In my opinion, No.4 is the best in your list, (followed by No.1, but only in speech). 2, 3 & 5 are not grammatically correct. You could also use 'Which one do you think is the best?'