How can different CAT5/6 cables affect sound.

It’s the analog signal that carries the digital signal (voltage fluctuations) over the copper Ethernet cable. 
Yes the data is transmitted accurately. However, we’re streaming music, not moving text documents over network. So in our systems the Ethernet cable is a digital cable. Just like any other cable - quality of the conductor, dielectric, shielding, connectors, etc. Everything matters for the quality of the signal received and processed by the component that’s fed by that cable. 
Your system will reproduce music just fine with a cheap cable as long as it works. You don’t need to spend a ton in Ethernet cables.
If you have a revealing system you are very familiar with, you will hear differences between Ethernet cables. I hear it in my system. 

Interesting thread…no science here but my experience is Ethernet cables can both make or not make an audible difference.  I feel it depends on many different variables.   Modem/router and their quality and power supplies, switch, optical isolation, Lan filters, power quality/conditioning, streamer quality and more. It seems to me it’s all about removing line pollution/noise.   If you have a revealing system and have done an excellent job cleaning up these variables the cable may not make a noticeable difference. If not, then the cable quality and it’s shielding should make a notable SQ difference.  I have a pretty revealing system and have cleaned up the above variables.  I have tried several different low/mid level ethernet cables and have never heard a SQ difference.  Now for those with super high revealing expensive systems with very high end cables improvement may be gained.… I don’t have experience at that level.   I have made a few changes and ordered  2 different pairs of higher end cables to try one more time to see if improvement can be heard.  Note:  I have heard very noticeable differences in improved SQ with all other cable types especially upgrades to USB and IC’s.

Is there a sonic difference between Cat5 and CAT6 cables?  Probably, but whether or not the average man can hear the difference, probably not. If all things construction are the same and the copper inside is identical, the change would be really really small. Heck,  I’m not sure even my dog could hear the difference and he’s a lot younger than I am.

@richardbrand ​Switched  Ethernet typically does not use CSMA/CD (Carrier Sense Multiple Access with Collision Detection) for its primary operation. While CSMA/CD is a fundamental part of Ethernet technology and was essential for early Ethernet networks using hubs, it is obsolete in modern switched Ethernet environments. 

TCP/IP guarantees bit perfect delivery. Packet sequencing, checksum and other header data answer the remaining questions about dropped, deformed or other anomalous packet behavior. When i was first introduced to TCP/iP in the late 1980s I was overwhelmed at everything the protocol did compared to competing non-routeable protocols like NetBEUI and IPX, but it became very clrar very shortly that TCP/IP was the future.

When Microsoft made its big push into networking, it threw tons of money into free training for Microsoft Certified Systems Engineers. And the class that separated those who would make it and those who couldn't? TCP/IP.  I took the week long class in LA - MS flew me from Seattle, housed, and fed me on their dime - with the provisions that if you failed, you wouldn't get reimbursed until you passed. Highly motivational. We had over 20 people in that class and about half failed the exam on their first try. It was a tough class, their toughest, and luckily I passed and became MCSE #410. There are now tens if not hundreds of thousand MCSEs.

A few years later Cisco Systems created the Cisco Certified Network Engineer, a curriculum so challenging that one CCNE i knew said "Next time I'll do something easy, like medical school." He wasn't kidding. So I went into Systems Architecture instead, and the CCNEs essentially worked for me. I knew the network architecture and dealt with big picture stuff , budgets, and management, shielding the CCNEs so the could concentrate on building and operating a 5-9s global infrastructure with multiple Enterprise-class data centers.

But boil it all down, and Switched/Routed Ethernet and TCP/IP is at the heart of networking as we know it today. I still like getting my hands dirty, I pull my own cable, terminate all my own connectors, and am even a certified fiber splicer. And I am very confident about what networking can and cannot add or subtract to sound quality.

So I'll say it again, whatever SQ differences people think they hear, it has nothing to do with anything happening at Layer 1 Physical, Layer 2 DataLink, or Layer 3 Network Layer 4 Transport, Layer 5 Session, Layer 6 Presentatio or Layer 7 Application. Or the condensed and simplified 4-Layer model. It is all happening above that. The entire DAC process rides above all the networking, and the analog output simply isn't even in the same domain.