Max tables in a MySQL database

There are no server limits on the number of tables in a MySQL database. You will definitely have no problems with 160 tables, and you don't need to split them into multiple databases.

You will not gain performance by splitting your tables into multiple databases. If performance remains an issue, you could consider using per-table tablespaces in order to place some sets of tables on different physical disks.

according to MySQL reference manual:

MySQL has no limit on the number of tables. The underlying file system may have a limit on the number of files that represent tables. Individual storage engines may impose engine-specific constraints. InnoDB permits up to 4 billion tables.