Your second listing is not the result of the command at line 1. I assume you executed ldd on {QTDIR}/qt5/plugins/sqldrivers/libqsqlmysql.so.

The Qt Mysql plugin for your Qt version has been built against an older Mysql client. You need to either:
  • Install an older Mysql client (libmysqlclient16 at a guess). The deb pacakge in /home/seth are from a later Ubuntu version, but the 16.04 xenial packages are also API version 20.
  • Build the Qt Mysql plugin from source matching your Qt version. You will need the relevant Mysql dev packages matching the client you have.

Given that you seem to have your own local Qt 5.7 the second option may be easiest.

The missing libcrypto and libssl are from OpenSSL.