RG58/U (I'd recommend only the stranded conductor RG58C/U -- the solid conductor stuff is too fragile) has very little loss per 60-70', even on 28 MHz, when _matched_. The problem occurs when it is not matched. When used with VSWR = 10, as is the case on some frequencies with a G5RV, the loss multiplies and can become unreasonable.
RG8X ("mini-8"), which is only slightly larger in diameter than RG58 (.242" vs. .195" diameter), has substantially less loss, even when mismatched, because it has a far larger gauge center conductor (#16 gauge, vs. #20 gauge), and in coaxial cable, most of the loss is due to the small outside diameter of the inner conductor.
Having said all that, I still don't recommend running transmission lines through attics and walls, unless it is absolutely necessary to do so. I say this for a variety of reasons, after 37+ years of hamming and installing antennas both for myself, and professionally for others.
"Reasons it's a bad idea to run transmission lines through attics and walls, and it's a good idea to drill a hole and bring the line straight into the shack from outside:"
1. These lines require service and occasional replacement -- and require same far more frequently than, say, cable TV lines, because we're using them for transmitting and therefore stressing them a great deal more than just receiving does. The easier your feedline is to get at, for testing and servicing, the happier you will be.
2. Coaxial cable, or any transmission line, even the best shielded ones, can radiate and receive signals. This occurs primarily due to mismatches between the cable and its load, which are customary and often necessary. The G5RV antenna is a perfect example of one which is badly mismatched, by design, on many frequencies. As a result of the mismatch, there is a reflected "wave" of current that is conducted back down the feedline from the load to the source, and that current is conducted down the _outside_ of the shield, not the _inside_ of the shield, where the intended (incident) transmitted signal is carried. Thus, that "standing wave" isn't shielded at all. It radiates. You don't want that radiation to closely couple to other wiring in your home that is commonly found in the attic, walls and crawl spaces. You'll be sorry!
3. Antenna experimenting is the heart of the amateur radio hobby. What is perfect today tends to suck tomorrow (to put it bluntly) and we tend to make changes frequently. That's a good thing. The easier it is for you to completely replace your transmission line(s) when needed, the better. You may find yourself running a kilowatt next year, in which case RG58 will have to be replaced, because it cannot handle that kind of power. That's just one small example.
73 & good luck!