How has Anydice not been mentioned? No need to bother writing stuff up in Excel, just write "output [highest 3 of 5d10]" and it'll give you a mean of 21.46 with a standard deviation of 4.35 in less than a second. There's no need to write up an entire block of stuff for excel! Let me summarize his entire attack routine in a one-liner:

When attacking, my character gets to roll 5d10, and keep the highest 3 dice. Also, 10s get rerolled and the new value is added to the old. -
Code:
output [highest 3 of 5d[explode d10]]
For the "four new skills" you mentioned, it only takes four lines.

Then, let's say I get to choose between four new skills: One adds +5 to the total, one lets me roll two extra die, and one lets me keep an extra die, and one lets me reroll two existing die (not summing their values like with the 10s, just rerolling normally). How do I determine which one will have the greatest impact?
  1. output [highest 3 of 5d[explode d10]]+5, average 29.48, standard dev. 8.06.
  2. output [highest 3 of 7d[explode d10]]], average 28.17, standard dev. 8.40.
  3. output [highest 4 of 5d[explode d10]], average 28.32. standard dev. 9.04.
  4. And I don't understand what you mean by the fourth one. Do you (1) explode 5 d10 separately, (2) reroll the lowest two, then (3) take the highest 3 of those?