Can Borderlands class mods raise a skill past 5 points?

Solution 1:

Yes, it won't show up as 7, but it will work.

This can be verified by using Mordecai's bird of prey skill with his bloodwing and counting the number of hits the bird goes through before returning.

However, keep in mind that boosting any probability above 100% won't matter (like having more than 100% chance of shield penetration on trespass). The extra damage % will still count.

Solution 2:

What am I seeing here? I have 2 points in the Safeguard skill which boosts my shield, and 1 point in the Hardened skill which boosts my health. The Centurion COM that I have equipped adds +3 points to Safeguard and +4 points to Hardened, making an even 5/5 for both.
I note my max shield and health before, put one more point in Safeguard and Hardened to push them to 6/5 each, and note my max shield and health after.
Conclusion: If the COM's skill-boosts couldn't push the skills over their natural limit, my max shield and health would not have gone up.

If you conduct the same test that I did, note that sometimes the max shield and health doesn't update in pause, which threw me off for a bit.