I have been playing piano for several years and have won first place at many competitions and performed at major venues such as Carnegie Hall.
At first glance, I would suggest you use both hands to navigate this tricky 3-octave jump. However, if you are already playing things in your right hand, I suggest you use the fingering 5, 1, 2, 25, 1. When you get to play the third note with your index finger, don't press that note by repositioning your hand. Play that note by almost flipping your hand from the last note. This fingering is especially helpful because it creates momentum with your whole hand almost turning to eventually hit that middle C.
Take the fingering very slow until you can do it with your eyes closed (literally!. This will help with accuracy later). Then slowly speed up the tempo and you should be able to execute it flawlessly.
I hope that helped! Let me know if you are still having trouble.