You can't go above 5 in any of your skill points. It doesn't show that you have points into any of them but they are there. Also, you can't move on to another skill tree if you complete a skill using a class mod. If you only have like 2 points in a level of a skill tree and you use a class mod that adds 3 into it you still need to add 3 others in different skills to get the next set. If you want 5 points with a mod that raises your skill by 3 you need to only put 2 into it or else it won't affect it any more. That is why your ammo capacity stays the same if you try to get it above 5. There is also a glitch that makes it so you can have all the skills maxed out at the same time but I won't get into that unless you email me at Antlersonmyhead@gmail.com to avoid a patch.
EDIT: If you have a class mod which adds +1-4 to a skill you haven't put any points into, it won't do anything. There is actually a debate whether or not class mods can stack upon skills which are already maxed. I think that some skills can go beyond 5 and others cannot. You can test it with some skills but not with others.