Here is the same exercise you saw earlier only for the 5th string.
Keep your thumb flat and positioned about the middle of the back of the neck. This will give your fingers a better reach and keep them from laying flat on the fretboard.
Try not to lift your fingers more than a 1/4" from the fretboard. This will increase your speed since the higher you lift off the longer it will take to move back down. This will also make it easier for you to get a feel for the neck so you don't have to always look at the fretboard.
Don't worry about speed. It is harder to play slow and in time than it is to play fast.
The 4th String Exercise
Use the L.H. (Left Hand) fingerings shown below.
Play each note starting with open the string and move up the fretboard.
Say each note name as you play it.
Once you reach the 12th fret go back down in reverse order using the same fingerings & saying the note names.
Notice that you are using the same 3 hand positions as before with the other strings only with different fingers.
Once you have learned the names of the notes and the correct fingerings for the 4th string add the 6th and 5th strings. Start with the 6th string then the 5th string and finally the 4th. This is a also a great warm-up exercise.
Ever notice that your 3rd finger (ring finger) and your 4th finger (pinky) do not always do what you want them to compared to the other 2 fingers and your thumb? WHY IS THAT?
There are 2 nerves that come down each arm from your brain into each hand. The brain send messages along each nerve to tell your fingers what to do.
One nerve goes into your 3rd finger (ring) and also branches over into your 1st finger, 2nd finger and your thumb. The 2nd nerve also goes into your 3rd finger (ring) but only branches over to your 4th finger (pinky).
This means that the 3rd finger (ring) is always hearing 2 messages while your 4th finger (pinky) only hears 1 message and not what the thumb and 1st two fingers are being told. This is why your 3rd finger (ring) tends to feel stiff and may stick out while your 4th finger (pinky) tends to stick with the 3rd finger OR sometimes sticks out on it's own.
As you practice the string exercises using the techniques tips, repeated at the start of each exercise as a reminder, your fingers are learning to become more independent and do what you want them to as you gain more control.