Basically the difference between a GL4 and a GL5 oil is that the GL5 contains more EP (extreme pressure) additives. The differentials, because of the sliding motion of the hypoid gears, require these additives, the transmission and transfer cases do not (they do not contain hypoid gears).
On the other hand, depending on the formulation of the particular oil, the EP additives used in the GL5 oils, may attack the softer, so called 'yellow', metals, used in the transmission and transfer cases, for the synchromesh rings, hence the recommendation for a GL4 oil for those applications.
Now that I have explained the differences between the oils and the reasons why a GL4 is recommended for one area and a GL5 for the other - let's go on to the problem - there does not seem to be a wide range of GL4 oils available on the market.
If Quaker State says their GL5 oils will attack yellow metals, and you can find their GL4 oil, then by all means use it - I cannot find a GL4 synthetic where I am, so I'm using Exxon's Mobil1 75w90 GL5 synthetic in the transmission, transfer case and both differentials.
Here's what Exxon Mobil has to say on the subject ...
Excellent rust, staining and corrosion protection of copper and its alloys
taken from
Exxon Mobil's page for their 75w90 GL5 synthetic oil (bronze and brass are both alloys of copper), and for what it's worth, I've been running this GL5 oil in the transmission of my Suzuki Swift, whic requires a GL4, for many years, with no ill effects - I've even had the transmission apart to replace the bearings and the synchros are in fine shape.