Several years ago, a TV show that I loved aired in syndication. I taped all the episodes, and now people are asking me to send them copies. Can I legally charge these individuals $5 per episode and make some profit?
There are very few clear "black and white" situations in the law, but this is one of them! What you are suggesting is a fairly explicit violation of copyright law. Copyright law gives creators of original works certain exclusive rights. Pursuant to 17 U.S. Code § 106, one of those is the right "to reproduce the copyrighted work in copies" as well as the right "to distribute copies or phonorecords of the copyrighted work to the public by sale or other transfer of ownership, or by rental, lease, or lending."
Here, the copyright in the television show likely belongs to the studio that created the series. They paid the money for the actors, the writers, the set designers, and the videographers. They made these substantial investments so that they could exclusively sell the show to television stations and consumers.
You made a recording of the show, which is permissible on its own. However, you now wish to sell those recordings to multiple people and make a profit. This is clearly impermissible under copyright law, and could expose you to litigation if the television studio ever discovered your scheme and wanted to make an example out of your conduct.