Yeah, that won't work. Hopefully you didn't short anything out.
You need a balanced cable for the headphones, either 2.5 and then use the 4.4 adapter (they are generally a bit cheaper), or a 4.4 cable in your particular flavor to match your endpoint -- MMCX, 2-pin, QDC, etc. The difference is that the grounds are separated, where in a standard 3.5 cable they are combined (hopefully I got that right, I know someone will correct me if I didn't). Only the higher-end IEMs generally are available with a stock balanced cable, but that's not a big deal in most cases because you can replace them unless your set has fixed cables (there are some, like the Periodic line). You can find balanced cables on Amazon and AliExpress, and a lot of other places. I wouldn't pay a lot for one (about $20-$30 depending on where you're buying from) unless you have lots of spare income. If that happens to be the case, boy, have you come to the right website!
The two jacks on the bottom of the R5
are not the same! The benefit to "recabling" your headphones is that you can use them on standard equipment that doesn't have a balanced plug with another adapter. Yeah, you're going to have a lot of adapters.