Does BMW make 21" or 22" rims for X5. I haven't seen anything bigger than 20".

BMW does not currently make a 21 or 22" wheel for the X5.

There are aftermarket manufacturers that do though (BBS, AC Schnitzer, Hamann, etc.). Check with your local wheel & tire shop for the different styles.

The BBS 21's look really good, but getting tires is a problem. Only Pirelli makes tires for that wheel. The 22's look too big for the X5.

Get 22's
There are many aftermarket companies out there who make good 22 inch rims.