It's not a good idea to disconnect the battery while the car is running - that can cause electrical problems.
Battery testing is best performed on a fully charged battery using a battery load tester but you can get some idea of the charge state of your battery with a multi-meter - simply measure the no-load voltage (i.e with the negative terminal removed).
In addition to the battery terminals on the battery, there are at least two other connections that might cause your problem. One is the "Battery Safety Terminal" (BST) on the positive battery lead.
Another possible problem location is at the positive jumper connection under the hood (bonnet) - it can get loose and disconnect the battery.
It's labelled "THRU BULKHEAD UNION SPLICE" in the image below: -
(NOTE: The image shows the B+ terminal as a separate line but in many E53 X5s, it is at the union splice location)
Hope that helps...
