Where can I find the proper drivers for a Lexmark X5150 printer? I don't have an internet connection on this computer.
Whilst Lexmark has begun to support linux with a few of their current printers, unfortunately they did not produce one for your particular model.
This was discussed over at linux mint
If you have your PC in a small network containing a Windows PC you could use a technique such as I described in this Q&A to print to it if the printer was attached to the Windows PC.