Looks like you need to contact ASUS, as your laptop uses "ASUS SonicMaster Technology"
From the specifications, I cannot see that it supports 5.1.
Also, it uses nvidia graphics (from the specifications).
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Ok, I am seeing the Intel HD Audio device and driver but not the NVIDIA HD Audio device or driver. To be honest, I do not know what this means. Does it mean that, when control switches over to the NVIDIA graphics engine (in a game or whatever), the Intel HD Audio device and driver disappear and the NVIDIA ones replace them? It that's the case, then how does the NVIDIA solution get the EDID information to know what audio is possible? As I said, try connecting PC --> Receiver --> TV and see if this resolves the issue. If not, talk to Asus and find out what their solution is doing.
This issue comes up from time to time.
First of all, let me say that the correct path for audio/video is Devices (laptop, XBOX, etc.) --> Receiver --> TV. This will allow the Receiver to output 5.1 surround sound even if the TV in use only supports 2.0 (i.e. stereo). Modern receivers are capable of returning a hybrid EDID signal that has the video capability information from the TV (from its EDID) and its own audio capability information.
Now, as you are connecting it with this XBOX, you need to remember that this XBOX has a single active graphics engine and this simplifies the situation. In this laptop, on the other hand, you have the complexity of two active engines, the Intel engine and the NVIDIA engine. Both solutions have digital audio drivers and both solutions can support up to 7.2 output over HDMI. The question is: who is currently in charge when the EDID information is provided and whether, when the other is in change, they have this information to work with. Al is correct that you will need to talk to Asus regarding how they have designed this hybrid graphics solution and whether there is an issue.