There are some synthetic GL-5 75W-90 gear lubes that are fine in the AX-5 and AX-15 transmissions. The synthetic GL-5 gear lubes that are safe will say something like 'Safe for yellow metals' on the back label. I've never seen a conventional (non-synthetic) GL-5 gear lube that was safe to use though.
Not all synthetic GL-5 75W-90 gear lubes are safe to use in our transmissions... this one is NOT safe for use in a transmission because its additives are sulphur-based which is harsh on the "yellow metals" which means it is harsh on the brass gear synchronizers... http://www.valvoline.com/pdf/synpower_gear.pdf
This synthetic 75W-90 GL-5 gear lube IS safe for use in a transmission... Max Gear - Royal Purple
. Note where it says "It is non-corrosive to soft yellow metals (brass, bronze, copper, etc.) and synchronizer safe."
And yes, the manufacturer (Aisin) of the AX-5 and AX-15 did indeed approve synthetic 10W-30 motor oil several years ago. As said above, the actual viscosities of 10W-30 motor oil and 75W-90 gear lube are very similar. Motor oils and gear lubes are measured on two different viscosity scales so while those viscosity numbers are different, those two viscosities (10W-30 motor oil and 75W90 gear lube) are actually very close.