Just download the JAR Connector/J file from the MySQL Download page, unzip the file and use the filename which has "-bin" in it.
Also, make sure the AEM machine can connect to the MySQL Machine using "telnet" command. Or try to run a query from the AEM Machine to MySQL using any Query Tool installed on AEM Machine. Make sure to verify all configuration related to the driver and data source in the AEM web console.
I used the latest 5.1.x version from here:
Unzip mysql-connector-java-5.1.49.zip, and select the JAR file with "-bin" in it. I understand that this file is already wrapped in an OSGi bundle. I spent several weeks troubleshooting this issue with Adobe Support. I hope this helps.