If you two can become real friends -- the kind of friends who help each other heal by being honest and trustworthy and loyal -- then you'll both have someone to trust, whether or not you end up together romantically. And they're radically better at sex than they were 10 or 15 years ago.
They're good at their jobs, but it's not how they identify themselves.
By now they've done the whole "master of the universe" career-building thing, so they've gotten really good at what they do.
But they've also figured out that it's not the only thing that gives them identity, and isn't the most important thing about them.
If you're a straight woman getting divorced, you might be afraid of what's going to happen. And if so, there can't be anyone good to date, right? One of the secrets you don't find out until you're back out there again is that men in the 35-55 age range are high quality, and highly attractive. (Unless they don't, which I'll cover later in "The Dude Who Never Learned.") They're really happy to be with a woman who can carry on a conversation, who is interested in the things they're interested in (but can teach and learn new things), who's funny and who thinks they're funny. They like that you're a good mom, if you have kids. If they have a CPAP machine to help them sleep, they may be too embarrassed to use it when you're staying over, but a gentle nudge from you will let them know that there's really nothing hotter than a full night's sleep.
(And it's not just their yummy greying hair.) Whether they're divorced like you or never-married, guys over 35 are radically better than you think. If either of you has insomnia, it could be compounded by the sleep apnea.