Checking directly for uniqueness of a 5000-character string is going to be pretty expensive, no matter how you implement it.
I'd suggest computing a hash, storing that hash, and computing uniqueness on that hash. This is almost the same thing, but does introduce the opportunity for a hash collision, where two different values result in the same hash.
The likelihood of a collision will vary with the hashing algorithm: MD5 has a 1 in 2128 chance in a collision. SHA1, and SHA256 each provide better protection against collision, but are slower/more expensive.
For example: You could create a computed/virtual column with the
MD5() function, then create a unique index on that column. This won't guarantee perfect uniqueness, but is likely unique enough for most purposes where you have a 5k chunk of text that you want to keep unique.
With hashing, if two different, unique strings have a hash collision, this would prevent that second unique value from being inserted. However, two identical strings will produce the same hash. So the problem with a weak hashing algorithm is that it would be too aggressive in preventing dupes when it shouldn't.