You caused the clog, you pay for unclogging it.
$95 doesn't seem unreasonable for a plumber to come out.
If you had called a drain cleaning service you would have paid about the same give or take. You can call around and confirm that.
As for the 5 minutes, I'm reminded of the story of the building owner that had serious electrical problems and called an electrician. The electrician looked over the situation, opened the electrical panel, replaced a part and handed the building owner a bill for $2000.
The building owner was astounded. "Took you five minutes and it didn't look like much of a part. How much does the part cost?"
Electrician: "$10."
Owner: "Then what is the $1990 for?"
Electrician: "For knowing where to put it."
The point being, had you known how to unclog the drain, you could have done it for free. Needing a professional cost you money. And plumbers ain't cheap.