I'm very excited that this show is back.
Maxter, I think you can start with this season and be fine. I didn't start watching until the beginning of the 4th season, but I caught on quickly enough. There will be some background information that you won't be aware of, but for the most part I do not think it will affect your enjoyment of the show. There seem to be a number of people on this board who watch, and I'm sure if you are unclear, someone here will be more than willing to help with details.
The "boyfriend" who is "all over" Chloe is actually her ex-husband Morris. Chloe called on him to help her at the end of last season and it appears that he is working at CTU full-time now. They weren't involved at the end of season 5, but it looks like they are now.
I will greatly miss Logan and Martha, both of whom really made Season 5 for me.
On another note, I am thrilled that both Bill Buchanan and Karen Hayes are back, and that they are now married, nonetheless!
Hope it will be a great season.