How to transfer videos from my HP laptop to my iPhone 5s?

I have videos that I took at a concert on my HP laptop and want to put them on my iPhone. How can I do this?

Also my iTunes account isn't set up on this specific laptop

You shouldn't need an account, just itunes and your iphone plugged into your laptop.

If your video is already mp4 video, you can import the mp4 video into iTunes at first. Connect your iPhone to computer through USB cable, iTunes will recognize the iPhone automatically, and then go to iTunes menu 'File -> Sync iPhone', the video will be transferred to iPhone.

If your video is not iPhone compatible mp4 video, you can follow this step by step guide to convert and sync the video to your iPhone, it's easy to understand and works pretty well for me.
http://www.dvdtoiphone3gs.com/how-to-play-dvd-video-on-iphone.html
Hope it helps. Contact me if you have any other question.

If iTunes can't do that, you can use some third-party tool to do that.