Let me also third the original recommendation of certified pre-owned. We purchased a used 2013 335I fairly loaded including the M sport package (sport suspension, 19" staggered wheels, etc.). A note on wheels/tires...if you purchase a 3 or 5 series with the two different size front and rear wheels, you can't rotate front to back. You can side to side. I wasn't aware of that when we bought and those 19" replacement tires were $300 each....just something to consider.
Anyway, the '13 still had quite a bit of factory warranty left so we didn't opt for the CPO on it. It also was not an X-drive vehicle.
We replaced it this past December with a 2016 CPO 340I with X-drive. It has basically everything except the heads up display (which I really miss) and those dang expensive 19" tires (18" all around, same size and can rotate...and about half the cost). Even though it was used (2,300 miles on the clock...hardly used), with the X-drive we thought it would be better to have that extra added warranty just in case. BMW had some issues with the X-drive in the beginning but seems to have worked out the bugs. I LOVE IT! You never know it's there but is when you need it. We don't get snow but the wet/rain assistance is greatly appreciated.
In 2014, we found a CPO Audi S4 when we found our '13 335. The S4 is a beast but a bit out of our price range compared to the '13 335 we had found. Sure did love driving that Audi. Fast forward to November last year. We again looked at a CPO S4 but we had been driving our '13 335 for over two years. It was an eye-opening experience. We came away realizing we made the correct choice with the BMW the first time. It also seemed that our '13 had carried it's worth over our ownership verses the S4 we were considering which was newer but with about the same mileage. The BMW was still worth more than that S4 and it drove/rode/handled better (to us) than the S4.
Some things to consider: BMW changed their maintenance plans extension with the 2016 model year as well as a complete change on the 2017 maintenance. The 2016 vehicles came new with full maintenance for 4 years/50K miles. However, they stopped transferring that to new owners when it was traded. You can purchase ($750 or more depending on model) to re-instate the maintenance but it's not automatic on used/pre owned/CPO 2016's. For 2017, ALL BMW's come with a 3 year, 36K miles basic maintenance plan (oil changes are the only thing included). I know you are looking at 2011-2013 range but something to consider if a '16 or '17 catches your eye.
Find one with M sport or sport suspension if you can. It changes the ride/handling/comfort to the good.
Consider the 3 series (335I is the inline 6 2015 and prior and 300hp...340I is the inline 6 2016 to present with 320hp) while looking at the 5 series. We looked at the 5 a few times but for the size, we couldn't tell that much more room. It was larger but in our thoughts not that much larger for the extra cost between the 3 and 5 series. We drove a turbo 4 X-drive...nice but that inline 6 is the bees-knees.
Good luck in your search. We do have a good dealer in Knoxville (Grayson BMW/MINI) if you are interested and not that far down I-75 to come down for a look-see.