The CVT in the Civic has been very reliable since the 2016 model year. Earlier versions had some issues though. But an 05 definitely doesn’t have the CVT.
I bought an LX 5 speed new the first year of this generation (2001). The drivetrain was flawless...everything else not so much. I had issues with the front suspension (clunking) and could not get any appreciable airflow out of the lower vents...feet froze in the winter. The a/c was marginal at best and the rear shocks were tuned poorly resulting in a bouncy ride on less-than-perfect roads. I understand that the 1.7l was prone to HG failure also. I wasn't a fan and sold it in less than 18 months.
We have a '12 Civic that our daughter uses. I've replaced the blower fan already but it's still noisy (better than it was though) and weak. The AC is fine but not like my car or my wife's where it can get the interior so cold you often have to turn the fan down because it gets too cold .