No!
And here's a sneaky data plan killer many totally overlook: MMS!
Consider that sending any image or video that you send via SMS/MMS will always be sent via mobile networks. Even if you're tightly wrapped into a strong WiFi bubble like at home or at work. SMS/MMS are always sent via mobile networks. Eating up your data plan real fast!
So, to the OP: forget sending photos and videos via SMS/MMS totally! As in: completely! Use only internet apps when in a WiFi like eMail or IM (Instant Messaging, like Kik, Line, Tango, Viber, Telegram). And Dropbox. Dropbox, or similar, is your friend. You can set it to sync only when you're in range of a (specific, if you're particular) WiFi hotspot. Again, like at home or at work, etc.
Oh, and you can go wild on pure text SMS if you get an appropriate contract, because those are microscopically small files. MMS messages, however, are at least hundreds but usually thousands of times larger files. And they count as mobile data.
So it looks as if you're never going to be using the S5 to its full potential, OP. Not even close.
I would go for a refurbished S3, under warranty, if I were you and get a much better data plan. Mine is 1,2GB/month. With very light mobile use I can manage to stay within that range. But only just. No live streaming video News, sports games, or movies on mobile! Ever! Even though my phone could handle it just fine. My wallet can't. Or at least won't.