You have results oriented questions, but we only know a bit about your goals. Do you want the 2 and 12 to have equal probability? Should the total of the probability to the left of the 5 equal the total of the probability to the right of it?
The last time I tried to shift the probability curve around, I determined that my best approach was to change dice based upon training and talent levels. A weak PC with no training trying to do something would roll 2d4 while a strong PC with a lot of pysical training might be rolling 2d12. I added an exploding die mechanic (if a die hit the maximum value, you added a die and subtracted 1 from the result) and a few other tweaks and ended up with exactly what I needed.
Roll 1d20, reassigning the numbers above 12 as follows:
The following may be better as it has actual fives in it:
In any case the reassigned numbers need to add up to 22 and the total of all the numbers needs to add up to 100
If you want 5 to be the most likely number, you could also roll d% and replace the numbers above 12 with seventy-five "5"s, eight "4"s, and five "3"s