Do Uber cars have enough space for 5 pieces of luggage?

Yes, UberXL and UberSUV should. Depends on how many passengers

There are two primary sizes for Uber cars.  UberX and UberBlack offer sedans that can hold up to 4 passengers.  UberXL and UberSUV offerSUVs that can hold up to 6 passengers.  There is a cargo/trun space with any of those options.  

If you have fewer passengers than the capacity, you an stow luggage in empty seats, which will give you more space to work with.  So if you are the only passenger on an UberX, you will have three additional seats and the trunk space, which can probably fit 5 pieces of luggage without a problem.  

I am not sure how many people you have in your party, but if you order an UberXL, you will receive a full-size SUV.  If you are looking at 2~3 passengers, 5 suitcases or bags should fit.  For more information, please refer to this RideGuru article:

How much luggage can I bring in my Uber/Lyft?

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC