Are there any difference between the FFT magnitude of a signal and average FFT magnitudes of the signal broken into multiple frames?
You would consider sectioning the overall data into smaller FFT frames for the possible reasons:


you are interested to know that for certain durations of time (length of ye FFT sections) which frequencies were active
there are not enough hardware cycles or resources to carry out a bigger FFT


If you are only interested in knowing what frquencies were ever present in the signal in it's entire duration and you have computation resources to carry out bigger FFTs then yes, you can carry out the FFT of the entire signal itslef. The bigger the sample size of signal duration in time domain over which the FFT is taken the better the resolution in frequency.

For the case you mention you would need to average out by 5 the result of the bigger FFT