Yes you can do it. You just have to make sure you highlight the page before you paste the subform. Copy the subform, select the page (make sure you have the small squares around the edges) then paste the subform on the page.
What you have is the subform is 'floating' above the tab control.
Also, be aware that adding 5 subforms to a single form will make the form take longer to load. I created a form very similar to the one you are describing. After the customer had been using the database for a month it became very slow to load.