As has been said, the pulse will remain constant, so you only need to worry about how many beats you count in each measure. But in the 3/8 measure, you want to compare the length of the 8th note to the 8th notes in the other measures. Instead of thinking about the quarter note getting the beat there, think of the 8th note getting the beat. You could also think of it is half of a 3/4 measure.
5/4 is really a time signature that is subdivided into a group of three beats and a group of two beats. (It could be 3+2 or 2+3) You will see this visually in the music. The measures I took a look at were be grouped as three, then two, but I didn't check to see whether or not that was true for every 5/4 measure in the piece. This grouping will give beat one the strongest pulse and beat 4 a strong pulse, but not as strong as beat one. Hearing that second strong pulse in the measure will help to keep the feel right and help you keep track of how many beats have gone by.