What are the effects on filtering upsampled data without interpolation?
How "bad" is this?


It's not too good.  What you are doing is equivalent to upsampling by a factor of five (i.e. inserting four zeros in between every sample), and then filtering it with a filter that has the impulse response [1, 1, 1, 1, 1].  The picture below shows the frequency response of this filter.



The signal aliases introduced by the upsampling are centered at 0.4 and 0.8, so the good news is that the filter has a null at the center of the aliases.  The bad news is that unless the signal has a really narrow bandwidth, the signal aliases will be much wider than the nulls, and a lot of alias energy will distort your signal.


  Is my only option to design an interpolation filter during upsampling, and if so, can anyone lead me to good references on how to design such a filter?


If you want to understand how to design a low-pass filter then I would suggest learning about windowed sinc functions.  If you just want to get a filter that works then I would recommend installing Octave and using the fir1 function to design the filter.