LITE-ON 24102B, Compaq 5QSB

I have a LiteOn LTR-24102B with firmware 5QSB that is installed in my Compaq computer. I would to upgrade to 5S59 but the 5s59.exe can only upgrade if the current firmware is between [5S01-5S9Z], (5QSB not included).
If it’s possible, is there any other way to do the upgrade?

First of all I installed the dos f/w cs5s07.exe, see link

and then upgraded the normal way