Mine is a 1999 Limited. It is in "good" condition [Not excellent cause I don't have many service records]. 105,000 miles. Many extras. Looks almost new.
Anyways, according to kbb.com, the private party value is $5,100
I have seen dealer ads for 97'* - 99'* go for at least a couple grand more than this at dealers.

I know for trade-in I would not get very much. That is why I want to private party.

Aside - I am maybe selling it cause I need the money [Juggling finanaces] and it is time to get something a little newer with less miles. I would take the cash and pay off a few bills and use maybe $1500 for a down payment. Maybe another LeSabre or bonneville. I wonder if anyone here has ever owned a bonne?

Just as a little comparison, My parents just sold a 2001 LeSabre Custom, 57k on it, for $6000 even. If you want pictures and options, check this link.

Also, this was in Binghamton, NY 13901 if you want to compare KBB values.

But I think that starting at $5000 is not a bad starting point, but just consider you will get lower offers, so you should decide on a bottom line price for it.