The Federal court system is divided into circuits [1]. Circuits are further divided into districts (eg Eastern District of Texas). In sparsely populated, large areas there districts may be further subdivided into divisions. The idea is you shouldn't need to drive 6 hours to get to a Federal judge.
Each district has an Appeals Court that sits above the District Court so that's what "Fifth Circuit Court of Appeals" means. Above all the circuit appeals courts sits the Supreme Court. Additionally, each circuit has a single Supreme Court judge who is available to hear emergency motions from appeals court rulings. That judge can rule on the motion or refer the matter to the entire Supreme Court.
Judges reflect the politics of the state they're in because of the blue slip system [2]. Presidents nominate judges to Federal courts. A Senator from that judge's state by tradition (ie there's no law for this) essentially can veto that nomination.
Federal district court judges have the power to make rulings and issue injunctions that affect the entire country.
So in Texas we have a perfect storm for judge shopping and a forum to push conservative views through lawsuits. Texas is a large state so the districts are divided into divisions. A division might only have 1-2 Federal district court judges. So if you nominally establish a business in Amarillo, TX you know with a high degree of certainty what judge you'll get when you file a lawsuit. With certain questionable tactics, you can know pretty much 100% what judge you "randomly" get assigned.
This is called "judge shopping".
It's why all the patent cases are litigated in the Eastern District of Texas. It's why any anti-abortion lawsuit always ends up in front of Judge Matthew Kacsmaryk [3] in the Northern District of Texas (eg [4]).
So the Fifth Circuit is conservative because Texas, Alabama and Louisiana are conservative. Conservative judges are usually viewed as more friendly to lawsuits attacking any sort of government regulation. Even if the Fifth Circuit Court of Appeals doesn't rule in favor of the cable companies, the matter will go straight to the Supreme Court. This current Supreme Court has shown themselves highly likely to take up the case and intervene, probably in favor of cable companies.
[1]: https://en.wikipedia.org/wiki/United_States_federal_judicial...
[2]: https://en.wikipedia.org/wiki/Blue_slip_(U.S._Senate)
[3]: https://www.txnd.uscourts.gov/judge/judge-matthew-kacsmaryk
[4]: https://www.npr.org/2023/04/07/1159220452/abortion-pill-drug...