Your Galaxy S5 has either 16GB or 32GB of internal memory.
You need to buy a "microSD" card to slide into the empty slot inside your phone next to the battery. It is REALLY EASY to do. I've attached a YouTube video if you're able to see it with your sick computer. If you can't see the video, just remove the thin plastic back cover with your fingers and you'll see the slot that the memory card slides right into. Push it in until it clicks. Replace the cover.
Samsung Galaxy S5: How to Insert a Micro SD Card - YouTube
I suggest either a 32 GB or 64 GB size should give you more than enough space. 10 or 15 dollars at Amazon or can buy locally. Get a decent brand like Samsung or Sandisk.
After it's installed just need to move the pictures/movies to the new card. Google that for instructions, it's also easy.
You might want to buy two cards. One to leave in the phone for extra storage and one to put away for safekeeping of your photos. The card is tiny, about the size of a fingernail.