Streaming movie from Galaxy S5 to TV, through laptop?

**Summary**: I want to stream Google Play movie from Android to HDMI/VGA/Composite TV, possibly through laptop. I have no idea whether it's possible or not but I'd really love some insight from some more knowledgeable people on. More in depth: I have a Galaxy S5, unrooted, that I absolutely love. First smart phone, I've been living off of a talk/text only phone previously. I also recently came home for the holidays to discover that my sister hasn't seen the Lord of the Rings! I figured I'd be smart, and use my Google Play account (with all three extended editions) to stream it through my laptop, and laptop to TV. Well, the internet here is very poor, I guess my parents get about .6 MBps? Anyways, video streaming kept buffering/loading, so I tried to move over to my phone, which has all three already downloaded into internal storage. Couldn't find a way to stream from phone to TV, the USB port wasn't gonna work. I don't have an adapter, but I do have my laptop. I tried pulling the downloaded .wvm file from the phone, but because yay DRM, that's a no go. I've done some searching, and while the AndroidScreencast project seems promising, it says it refreshes at about 5 FPS, so not very good for media streaming. So I have a phone, a laptop, and a TV. I can connect the phone to the laptop by USB or Bluetooth. Laptop to TV via HDMI or VGA. Is there any way I can play the movie on my phone, have it feeding the video to the TV/laptop, and then to the TV?