Not sure what you are trying to achieve with the increasing speed. Also, I'm guessing the speedo on your treadmill is broken, as doing intervals at 10mph would be about the speed for a sub 40 min 10k runner.

There's two basic types of speed sessions:

Intervals. To do this run at your 5k pace for a short distance (try 400m to start with) multiple times with a short break in between (e.g. roughly 50 to 75% of the interval distance). The intention is to run all intervals at a consistent pace, and the last interval should be very hard to maintain the pace throughout. This takes a bit of practice, so it may take a couple of attempts before you find the right pace. Try starting with 5x 400m and then adding another interval every few weeks once you've found your target pace (you can also modify the length of the interval upto 600m, whilst reducing the number of repeats to cover a similar distance - e.g. 6 x 400 or 4 x 600). For a 10k runner, you probably don't need to go beyond 600ms per interval.

Tempo runs are the other speed work, where you run at a pace equivalent to your current 10k speed for a longer distance but not the full race distance (e.g. 3 miles at 10k pace plus running a mile before and a mile after to bring the total up to five miles).

I wouldn't worry about pyramid intervals and any of the other more complicated routines at the moment. You start using these once you've plateaued with the simpler approaches. Do one of each of these sessions mentioned above per week, plus a couple of easy runs and you should see a marked improvement after a couple of months.