I think the OP is trying to say the engine cranks longer than expected. Hot Cold?
I think what I would like to see is starter draw (AMPs and voltage when cranking) results.
Cyl power balance (Are all the cylinders firing and contributing to output)
Compression results

These are only to establish a baseline of engine starting and running condition. Slow idle condition has many contributing parts/conditions.
IAC, ISM, TPS, throttle body issues, injectors with low / poor patterns, Etc, etc as well as mechanical contributors. Let eliminate a few issues with some base lining.

If the CPS signal is weak, then the engine "Hunts" for the firing order and where and when #1 cyl and #3 are at top dead center. The engine will not fire as it has no idea which cylinder to fire off. The CPS sensor tells the Engine control system when the cylinders are at TDC and then it fires off a primary signal to the corresponding coils. If the signal is weak the engine will continue to crank until the signal is read.
Diagnostic software will display these signals on cranking.
Makes sense?

__________________

2005 X5 4.8IS
The Blue ones are always FASTER....

Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green