Animisha I would prefer to play the lowest note G with F5 and the highest note B with F1, so the jump from this B to G is not that bad. But what to do with the D and G between those two? If I play them with F3 and F2, it means that I either need to look at those keys a lot and cannot look at my score, or that I risk making mistakes when jumping.
Because my hands aren't large, when I see a phrase like this, I don't think of trying to stretch my hands, and because of the pedaling, I don't think of rotation b/c there's no need to maintain legato. Instead my instinct is D/F5, G/F2, B/F1, and then a jump from B/F1 to lower G/F5, followed by a return to D/F5. The hand can stay nicely compact and well-centered throughout with good wrist motion. But in order to do this, you have to be able to make F1/F5 jumps of a 10th blind, and F5/F5 jumps of a 4th easily.
The rotations that Sam S and BartK/WieWaldi suggest also work, of course, but for me the thumb-over rotation on the left hand to F2 is slow, and the pivoting that WieWaldi shows causes me strain; it stretches out my hands too much.
Probably about 15 years ago, my proprioception had waned quite a bit from lack of playing, and I tried to compensate for it by stretching out my hands a lot, to minimize both the number and size of jumps that I had to do. In retrospect, I think that was a mistake, since it created quite a bit of tension in my hands, plus I developed the bad habit of keeping my hands stretched out. Lately I have been working on keeping my hands relatively compact (and relaxed) while nailing the jumps, and everything feels better, plus I can play faster, too.
My sense is that you need to work more on your proprioception. That could just mean playing these few measures repeatedly so you needn't look at your left hand at all, but I think it would be better for you to find music in which you have to make smaller jumps, both using F1 and F5, but also other fingers. For jumps using F1 and F5, perhaps a 6th or 7th, but not legato, and don't stretch out your hands; make a real jump! - first occasionally, and then frequently. Eventually I think that you will find jumps of a 10th, 11th, and 12th straightforward to do without needing to look or stretch out your hands a lot in order to make the jump smaller.
For other fingers, something which requires you to make jumps using only F5, or only F3, would also be good.
Animisha, I've been puzzled by the fact that you never see improvement after a decent night of sleep. Perhaps it's something to do with aging, but I'm beginning to wonder if maybe part of the problem is that you're trying to learn too much - make overly large leaps both figuratively and literally - in one go. This thing I describe about learning to make progressively larger jumps was taught to me quite slowly, probably over a period of a few years, using a variety of short exercises and short- to medium-length (no more than 5 pages) pieces. I didn't realize how slow-and-steady (nor how carefully planned) the progress was, until I quit and occasionally tried to learn pieces on my own. Pieces that seemed like they should be easy were fruitless struggles, because there were techniques and skills that I either didn't know about or hadn't fully developed for all situations. And it turns out that just being able to read the sheet music wasn't nearly enough for me to know what was actually straightforward with my skill set.
