H.264 .mp4 files on 5 bitrate ( is killing me )

File Size = Bitrate*Time

The bitrate slider is pretty much your one control over video quality and it's in direct relation to the file size. The higher the bitrate (quality) the higher the file size. It's up to you to determine the level of quality you are comfortable with and at the lowest file size.

7.2GB for a 2 hour long video sounds reasonable, if not low to me. 5 Mbps is quite a low bitrate for a 1920x1080 video.

The trouble is that your starting point is an extremely low bitrate. Almost all the data has already been removed from that video when you downloaded it, and when you create a video in Premiere it isn't going to just pass-through the video quality exactly how it was and splice it together. It's going to re-encode your video from scratch. If you match the original bitrate of your media, you're going to add another pretty significant generation of compression loss to it. You're taking super compressed video and trying to super compress it again. To even retain what little is left you'd need to increase the bitrate a bit.

Just out of curiosity if we want to figure out what the bitrate of the original media is (in case you want to achieve a similar file size):

File Size (1GB) = Bitrate (X) * Time (2 Hours)

Conversions: 1GB = 1000MB = 8000Mb. 2 Hours = 120 Minutes = 7200 Seconds.

8000Mb = X * 7200 (seconds) --> X = 8000/7200 = 1.1 Mbps (very, very low)

In an ideal situation, you start with a high quality video and then at the end of the process you compress it down.

The ideal starting poing=high quality video:

This is the video you are starting with: