There really isn't a "right way" or "wrong way" to play those Long Pattern Pentatonic Scales. Me? I will typically assign 1 finger per fret, meaning that is I am playing frets 5 & 8 on the low E string, I will play 5 with index and 8 with pinky.
For a stretch like frets 5, 7, 10, I will adapt my fingers accordingly: 5 = index, 7 = middle, 10 = pinky and move on to the next string. Now, if you are then playing fret 12 on the same string, you can work on sliding 5-7 with index, 10 = ring, 12 = pinky, OR 5 = index, 7 = middle, 10 - 12 = slide with pinky. If the 4 notes are close to each other, say on the high E string, I will play 12 = index, 15 = middle, 17 = ring, 19 = pinky, OR again, incorporate a slide in there somewhere.
You see? There is no definitive way, so practice ALL possibilities.
As far as descending from high E to low E, and whether or not to pick up your entire hand and place it on the next string, it depends on whether or not you are using a slide in there somewhere, or a long stretch. Again, play whatever is comfortable for YOU.