As I grouped five notes into one pattern (starting from the D# in the right hand, using fingerings 21235), however, every time the D# falls on a different beat, it's difficult for me to count 3 notes in one group accurately.
I don't fully understand what you are having trouble with, can you clarify a bit? 16th note triplets = three notes per normal eighth note. You have the eighth note pulse going steadily at the start of the first bar in the picture. Just fit the triplets into that existing pulse. Maybe you can be slightly elastic with the tempo on the triplets as it is a decorative figuration.