If I run CAT5/6 cables parallel to electrical cables, is it possible to shield the cables with copper tubes to stop interference?
You're hunting a snark.

People are constantly forgetting (or never learning) that network signals on Cat5e or Cat6 are differential twisted pair signals, which means that they are composed of a difference in voltage applied to one end of a pair of wires that are twisted together and received by looking at ONLY the difference in voltage on the receiving end. If an interfering voltage couples to the wires, it couples to both of them, resulting in a "common mode voltage" and has very little effect on the voltage difference between them. The twists also tend to make outside voltages nullify themselves when they try to couple. It actually works, quite well.

As such, while it is good practice to maintain separation, it is very rare to have any significant impact from 50 or 60 Hz powerlines on 100+ MHz network signals. I say that as a person who had miles of network cable (in 100 meter or less chunks) attached to switches that reported error rates. Many of those cables were, due to the realities of  installing new-fangled network into old buildings without ripping the old buildings to shreds, parallel to power wiring for long distances. Short of actual damage to a cable, the error counts were typically zero.

Given the opportunity in new construction, sure, put it in the next stud bay, (i.e. 16-24" separation) but foolishness like running it in copper pipe is foolishness (you can get foil-shielded cable instead of unshielded cable [FTP .vs. UTP cables,] or just run plain steel EMT conduit if you want to go there at all, and you don't NEED to, at least for "interference from powerlines") - I'm a big fan of EMT to prevent "interference from rodents" but that's a different issue.