Hi, you didn't give any info about your knowledge of the hobby, experience with selling or grading the condition of comics, what your time frame is etc
Sounds like you're off to the right start, just go thru them and note titles/issues. Even with 5000 that shouldn't take that long if that's all you're noting.
How aware are you of the various auction sites like Heritage/Comic Link & Connect, MyComicShop etc where you could either just sell the whole collection to them or have them sell it for you?
While I've never used any of them there's plenty of good folks here who have used them & others. If you haven't already, I would suggest going thru their websites to see their selling process.
I would think selling any major keys (ie GSX 1; ASM 50 etc) individually would be a good move.
Good luck