Since this is a solo instrument, I recommend two ways, both related.
- Learn to count 5:1. Start slowly, counting to 5 and clapping on every 1, and vice versa. This will give you an initial feel for quintuplets.
- Learn to count 5:2. Similar to the above, but get used to feeling a pulse halfway across the quintuplet. Do this in "both directions": count in five, clapping on 1 and the
&of 3; and count in two, placing the quintuplet accordingly.
When both of the above can be done with ease, then, a few measures ahead of the quintuplet, start counting your music in 1 or 2, depending on the speed of the music and your comfort level with the 5:1 vs. 5:2 subdivision.
In the case where a single instrument, say, a piano, must actually play 5:4, then the best way I know is to begin by subdividing into 20 pulses to figure out where each note will be placed. Then practice slowly, speeding up only as the intuitive feel of the rhythmic relationships develops.
As a (finger drawn on screen, sorry) visual supplement to the answers by @Tim and @Aaron suggesting a subdivision of 20, the common denominator of 4&5, here is a superimposed 20 count over your posted example with quarter notes added below:
I find SEEING something like this is very useful as you can make a visual connection to where the notes fall. You might notice that after the shared downbeat the first 5&4 notes played are a flam with the 5 coming first and the last 5&4 notes played are a flam with the the 4 coming first. The 3rd and 4th 5 pulses are slightly off from being directly between beats 2&4.
Based in the visual, one way to conceptualize this rhythm in a non-accurate but ballpark way is to convert it into 16th notes, like this:
Like I said this is not rhythmically precise (it is actually grouped as 3,3,4,3,3) and some may disagree but it will give you a relatable way of playing 5 notes against 4 beats until you start to really feel the 5 against 4 naturally.
One last thing you can do if you do any computer based music is to program a 5 on 4 rhythm into a DAW with two different pitches or sounds and listen to it in a loop to help you get the feel of it,
Are they played on their own, or will your left hand be playing four q-notes against the five?
I suggest rather that instead of splitting into tiny units you go the other way. Feel a slow ONE.... in each bar. Set up a plodding walk tempo in your head. Tap your foot to it. Now practice playing half-notes, half-note triplets (three to each bar), quarter-notes, quintuplet quarter-notes... You'll find out what quintuplets FEEL like. It's not hard. Get your teacher to demonstrate.
It's just like in maths; adding different fractions. The first thing one does is find a common denominator. This will split both fractions into parts that have equal divisions. Adding quarters and thirds will need both parts to be changed into twelfths.
Here, where the normal bar is in 4, and the notes shown are in 5, the denominator is going to be 20. It sounds like a lot to count in a single bar - it is. But it's a good way to work out (slowly) where each and every note belongs. Writing out 1-20 and highlighting 1, 5, 9, 13, 17 will show where the tuplets fit for 5 against 4. Use a different colour for 1, 6, 11, 16 to show the original 4 count.
A metronome will be invaluable here - set very slowly! Set it for a 20 count, then tap one hand for the regular beats, the other for the tuplets. Gradually speed it all up until the original 4/4 tempo is reached - as designated by 1, 6, 11, 16. Then try the metronome just at 4 beats per bar, again starting slowly. Good luck!