De Lorenzo's L'Indispensabile, No. 5

The fifth exercise of L'Indispensabile uses the same five-note pattern as number 4, but it flips the pairs of notes which creates a significant challenge. The biggest challenge for this one at least in the beginning is more of a mental one, of wrapped the brain around the pattern. Once you become comfortable with the pattern the fourths should be carefully minded.
If you are new to this exercise, then it would be very beneficial to spend a little extra time on the printed version in C major before moving on to the other keys. You may even want to start this one at a slower metronome marking than you were using on number 4 and breaking it down into chunks will also be helpful. Throughout your practice, be sure to keep the tension low.

De Lorenzo's L'Indispensabile, No. 4

The fourth exercise of De Lorenzo's L'Indispensabile is designed to iron out irregularities between pairs of notes, working within a pentascale. Each bar is framed within a repeat sign, with directions that it should also be practiced without repeating each bar.

When beginning practice of this oeuvre, I recommend focusing your practice on #4 before moving on to #5-17, which are all some sort of variation on #4. Maintain focus on evenness of fingers and sound. In the early weeks of practice, it is advantageous to move through minor finger blips or irregularities in order to focus on success through the whole exercise. Often these minor issues sort themselves out over time, or they can be addressed with a bit of focused practice. I began my practice of this exercise at eighth note = 60. As with the beginnings of any technical development regimen, speed should not the highest priority. Rather, prioritize fluidity of motion with minimal tension. Speed will come with time.

Practice all of #4 in one key per day. Begin in C major, followed by C# the next day, then D, etc. This allows for regular practice of differing finger combinations. If desired, you can alternate by playing the first half of #4 (ascending) in C, second half (descending) in C#. Next day continue with D/E-flat. 

After establishing a familiarity with this exercise, you can begin to build agility by playing the first time at your regular tempo, and the second time at double speed. Only continue this as long as you are able to play fairly cleanly and without excessive tension. Do this on the ascending portion and then begin the descending portion by playing at the normal speed for both repeats. Then, when you reach the point where you had stopping doing the double tempo on the way up, resume adding the double-time repeat on the way down. You may even find that you can begin the doubled tempo at a higher pitch level on the way down than you could on the way up.

As far as range goes, I recommend beginning with the printed range of two octaves and fifth. As you ascend through each key, continue to maintain that range as much as you can without the technique falling apart or increased tension. I usually find that high B-flat is usually my limit at first, but it's perfectly reasonable to stop at any note that you decide is most comfortable for you. This means that as the tonal center ascends, the overall range of the exercise will decrease. I wouldn't recommend starting lower than whatever the pitch center is, but if you want to include the bottom of the range, I would do it in the following manner. I will use B-flat major as an example. Begin on third line B-flat and ascend to high A or B-flat as normal, then descend back to the starting point (the set that covers from third line B-flat to top line F). Then, continue the descending pattern until you reach low C. From low C play the ascending pattern until you have returned to third line B-flat. 

Once #4 is firmly under your fingers, exercises 5 and 6 are the next to work on.