5 years Bahrain Visa

Iqama / residence visa and 5 year visa / paper CPR are different things.  There are many threads on these forums which deal with this subject and you can use the search button.

And reading your post, I don't understand why, if you are working with a company in Bahrain, they haven't gotten you a proper work visa vs. a 5 year visa / paper CPR.

Paper CPR and 5 year visa does NOT allow you to sponsor family stand alone.  It is usually given if you have a Saudi Iqama and you want to live in Bahrain.  You need to get your family Saudi iqamas under your sponsorship and then when they come here, they can also get the same visas and paper CPR on the basis of those Saudi Iqamas.  And no, you cannot get the full Bahrain residency or CPR until or unless: you work in Bahrain and are sponsored by a company here, you set up your own company or you buy property and self sponsor.