To generate one permutation use random.shuffle and store a copy of the result. Repeat this operation in a loop and each time check for duplicates (there probably won’t be any though). Once you have 5000 items in your result set, stop.
To address the point in the comment, Python’s random module is based on the Mersenne Twister and has a period of 2**19937-1, which is considerably larger than 27! so it should be suitable for your use.