Agree with most everything already posted. For the record, I own a 2013 X5 35d (same E70 chassis but with the diesel engine) that I bought used in 2016 with just over 70k miles and it now has 171k.
Of all the vehicles I've owned, it's my absolute favorite. Has a solid feel to it and the diesel engine lays down addictive levels of torque. It's able to do things that no 5000+ lb. SUV should be able to do. That said, I've only been able to keep it going for so long because I am constantly tinkering with it, ordering parts from FCP Euro, and I put the diesel emissions stuff on a permanent weight loss plan, etc. Also note for your daughter that if the vehicle has the third row option, there is no space for a spare tire and tool kit. If no third row, it still may not have a spare (I had to buy the kit and add it myself). Run flat tires are trash from a performance/handling standpoint but could be a decent compromise if no spare available.
I can't speak to the gas engine itself but I'll give you the rundown of things I've had to do maintenance-wise to keep it going this long while making it a bit more fun:
- Full transmission service around 100k (honestly, probably waited too long and likely need to do it again now): dropped the pan and "mechatronics" module, replaced seals, solenoids, and filled with fresh fluid. I can't remember if the gassers have the same transmission but mine is the 6 speed from ZF (same transmission used in a lot of Ford trucks... a common upgrade is to use a transmission pan for an F150 because it holds more fluid and allows for a separate replaceable filter... the stock plastic BMW pans have an integrated filter and you have to trash the whole thing for a filter change).
- Transmission tune (xHP Stage 3)
- Changed front and rear differential fluid and transfer case fluid
- Complete suspension refresh around 150K (all ball joints and rubber bushings were shot, among other things): new struts and upper/lower control arms up front, new coil springs and shocks in back
- In the course of being deep into things for other maintenance, replaced water pump, thermostat, coolant control valve for the HVAC, several pieces of coolant hard piping that had become brittle, and various o-rings on coolant lines
- (diesel engine specific) Glow plugs, glow plug controller module, valve cover gasket, vacuum pump gaskets, new vacuum lines, vacuum reservoir, vacuum control valves for turbos, EGR/DPF/SCR delete and related ECU tune, new charge air pipes and upgraded aftermarket intercooler (boost leaks everywhere that had to be addressed)
- Various replacements / upgrades of interior components... for example, the interior passenger side door handle rubber turned into sticky goo, replaced with hard plastic aftermarket upgrade, deleted useless phone cradle in center console and closed hole with plastic block-off plate
- Lost count of how many sets of tires I've gone through. It's fun to drive but you'll want sticky rubber... not great for wear. Currently running Continental DSW06 Plus, about $1200 for a set.
Overall, perfect vehicle for me and if it goes up in flames I'm buying another diesel one in a heartbeat off of someone in one of the Facebook enthusiast groups that has kept up with maintenance. I know it like the back of my hand and have fun working on it. That said, would not recommend for your daughter unless you want to be constantly working on it and chasing down gremlins. A BMW-specific scan tool or OBD app is almost mandatory... ProTool is what I use and seems to be the most widely used.