Feedback on Dice Mechanics

I was looking to get some feedback on the basics mechanics for a homebrew RPG I'm developing.
Most checks will take the form of skill dice + attribute bonus + misc. modifier. Your dice can explode. This happens on a result of 6 (for poor, average, and trained skills) or 5 or 6 (for Elite Skills). When a dice explodes, you roll it again and add the results together. A die can explode multiple times. Attributes add a flat bonus to your checks. Average Skills roll 5d6, trained and elite skills roll 6d6, and poor skills roll 4d6
Example: Timmy rolls an Trained skill check (6d6). He rolls 6,5,4,3,2,1 (total=21). Since he rolled a six, he gets to reroll that dice. He rolls a 4, for a total of 25. If this was his Elite Skill (rather than a trained skill) then he would have been able to reroll two dice
If your highest two dice (including rerolls) beats the target difficulty, then you have scored a critical success.
Skills:
Inept 4d6
Average 5d6
Trained 6d6
Elite 6d6 RR
Master 7d6 RR
Grandmaster 8d6 RR
Epic 9d6 RR
Attributes
Poor -2
Average 0
Adept +2
Heroic +4
Mighty +6
Preternatural +8
Deific +10
To create a character, pick one Heroic attribute, one poor and 5 Adept attributes, with no more than three of your trained attributes being in the same category. Likewise, pick one elite, one poor and 5 trained skills in both the major and minor categories.
You can also reduce two attributes to poor to raise another attribute to trained. You still must have no more than three trained attributes in either category.
Physical:
Strength
Reflexes
Dexterity
Endurance
Athleticism
Mental:
Charisma
Guile
Intellect
Willpower
Intuition
Fortune
Some thoughts:
1)Is 5d6 too much? I like the idea of skills and attributes working in different ways, but with smaller numbers of dice, the jump between average and trained skills is just too much. The only things I worry about with using that many dice is a) the amount of times it takes to add the numbers and B)weighting numerical bonuses too much.
2) I really like the idea of expanding the reroll range on elite skills because it helps more at higher difficulties (i.e. it doesn't totally prevent you from failing at say difficulty 20 (which is average) but it doubles your chances of making a difficulty 30 check.)
3) Attributes have roughly half the effect the skills do. I like this because it emphasizes skills, which are more focused than attributes and so should have a greater effect.
Probability of Success Chart (20 is average, 25 is hard, 30 is very hard, 15 is easy.)
Difficulty 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11
4d6 4.6 5.6 6.9 8.3 10.1 12.2 14.6 17.3 20.6 24.4 28.7 33.6 39 44.7 50.9 57.6 65.6 71.8 78.9 85.3 90.6
5d6 12.4 14.7 17.3 20.2 23.5 27.3 31.4 36.1 41.1 46.4 52.1 58 64 70.1 76.1 81.8 86.8 91.1 94.4 96.8 98.4
6d6 26 29.7 33.7 38.1 42.8 47.8 53 58.3 63.7 69.1 74.4 79.5 84.2 88.3 91.8 94.6 96.7 98.1 99 99.5 99.8
6d6* 50.1 54.4 57.9 61.5 65.1 68.7 72.2 75.6 78.9 82.1 85.1 87.8 90.3 92.5 94.3 95.9 98.3 98.4 99.1 99.5
* indicates expanded reroll
Most checks will take the form of skill dice + attribute bonus + misc. modifier. Your dice can explode. This happens on a result of 6 (for poor, average, and trained skills) or 5 or 6 (for Elite Skills). When a dice explodes, you roll it again and add the results together. A die can explode multiple times. Attributes add a flat bonus to your checks. Average Skills roll 5d6, trained and elite skills roll 6d6, and poor skills roll 4d6
Example: Timmy rolls an Trained skill check (6d6). He rolls 6,5,4,3,2,1 (total=21). Since he rolled a six, he gets to reroll that dice. He rolls a 4, for a total of 25. If this was his Elite Skill (rather than a trained skill) then he would have been able to reroll two dice
If your highest two dice (including rerolls) beats the target difficulty, then you have scored a critical success.
Skills:
Inept 4d6
Average 5d6
Trained 6d6
Elite 6d6 RR
Master 7d6 RR
Grandmaster 8d6 RR
Epic 9d6 RR
Attributes
Poor -2
Average 0
Adept +2
Heroic +4
Mighty +6
Preternatural +8
Deific +10
To create a character, pick one Heroic attribute, one poor and 5 Adept attributes, with no more than three of your trained attributes being in the same category. Likewise, pick one elite, one poor and 5 trained skills in both the major and minor categories.
You can also reduce two attributes to poor to raise another attribute to trained. You still must have no more than three trained attributes in either category.
Physical:
Strength
Reflexes
Dexterity
Endurance
Athleticism
Mental:
Charisma
Guile
Intellect
Willpower
Intuition
Fortune
Some thoughts:
1)Is 5d6 too much? I like the idea of skills and attributes working in different ways, but with smaller numbers of dice, the jump between average and trained skills is just too much. The only things I worry about with using that many dice is a) the amount of times it takes to add the numbers and B)weighting numerical bonuses too much.
2) I really like the idea of expanding the reroll range on elite skills because it helps more at higher difficulties (i.e. it doesn't totally prevent you from failing at say difficulty 20 (which is average) but it doubles your chances of making a difficulty 30 check.)
3) Attributes have roughly half the effect the skills do. I like this because it emphasizes skills, which are more focused than attributes and so should have a greater effect.
Probability of Success Chart (20 is average, 25 is hard, 30 is very hard, 15 is easy.)
Difficulty 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11
4d6 4.6 5.6 6.9 8.3 10.1 12.2 14.6 17.3 20.6 24.4 28.7 33.6 39 44.7 50.9 57.6 65.6 71.8 78.9 85.3 90.6
5d6 12.4 14.7 17.3 20.2 23.5 27.3 31.4 36.1 41.1 46.4 52.1 58 64 70.1 76.1 81.8 86.8 91.1 94.4 96.8 98.4
6d6 26 29.7 33.7 38.1 42.8 47.8 53 58.3 63.7 69.1 74.4 79.5 84.2 88.3 91.8 94.6 96.7 98.1 99 99.5 99.8
6d6* 50.1 54.4 57.9 61.5 65.1 68.7 72.2 75.6 78.9 82.1 85.1 87.8 90.3 92.5 94.3 95.9 98.3 98.4 99.1 99.5
* indicates expanded reroll