This hose is part of the secondary air pump system on E53 X5 3.0 models. The secondary air pump adds fresh air to the exhaust to help with cold start emissions and to heat the catalytic converters and O2 sensors. A broken hose likely won't cause any reliability or drivability issues but may cause a check engine light or lead to premature failure of cats or O2 sensors.
This is a air pump hose manufactured by Rein (CRP) Automotive - the original supplier to BMW for this part, as well as many other hoses and lines. As the OEM it meets all of BMW's original design, fitment, and performance requirements and is TUV approved. OEM parts are the best alternative to more expensive Original BMW parts because they are virtually identical without the inflated price tag. This part has a two year warranty.
BMW Fitments:
X5 Series
E53 X5 (00-06) > X5 3.0i M54