The first question that needs to be addressed is in a perfect world with ideal amplification, will a 40Ω cartridge sound the same into a 5Ω load as a 47kΩ load?
Right up to this point I was in agreement with the prior text of this post. With this question we can safely say the answer is 'No.', assuming that the perfect amplification is voltage amplification. The question cannot be answered at all if current amplification is used.
If that is a static load (IOW, a resistor) then the cartridge will be making 4 orders of magnitude more work! That work has to come from somewhere, otherwise a new branch of physics is created 😉
So it will certainly cause the cantilever to be harder to move (stiffer) and that will affect how the cartridge 'sounds'. It won't affect the bandwidth of the coil in the cartridge at all- but will have an enormous affect on the mechanical aspect as the coil will have become a significant load with 5 Ohms loading it in turn. Also, the output level will be considerably decreased!