480 x 360 = 4::3 ratio (not 16:9)
Sorry, 480 x 272. 560 x 315 would be even better, but doubt I can keep the file size down at that resolution.
Screen resolution really has no correlation to file size in the video world. The only thing that really matters is bit rate, usually calculated in kilobits per second (kbps) or megabits per second (Mbps). File size is simply the bit rate multiplied by the duration of the video; screen resolution or frame size doesn't come into the equation. Frame size will only come into play on viewing the file, because the amount of data encoded into each frame will have to be spread around to fill the frame. Think of it as if you had a gallon jug that was full of water, and then you dumped that gallon of water into a kiddie pool. You have the same amount of liquid (in this case, our liquid is bits), regardless of the container size (in this case, or container is the video frame), it's just that the water won't fill the latter container nearly as much as the former. Apply this to video compression, and you're using the same number of bits spread around a larger container, so the end product is not going to look good, ie. the water will be shallow.
Back to file size and bit rate: all you have to do is use your video's duration in seconds and divide it into your desired file size either expressed in kilobits or megabits (not kilobytes or megabytes). For most anything on the web that's going to be below 1Mbps, I prefer to work in kilobits, because it's a little more accurate. So for your example:
Length of video in seconds: 260s
Desired file size in kilobits: 7MB x 1000 (to convert to kilobytes) = 7168KB x 8 (to convert to kilobits) = 57344kb
Bit rate in kbps: 57344 / 260 = about 220kbps
So, in order for your file to be about 7MB, you need a bit rate of 220kbps. Now, that's just for video; if you have audio, you'll have to consider that as well, and either subtract it from the video bit rate, or deal with a larger file size. In any event, 220kbps is pretty low, even for H.264, but you might squeak by at nothing larger than 480x272. You could spread those bits around a bit (no pun intended) less by going with something like 320x176, or if there isn't much motion in the video, the 480x272 size might work. I've gotten decent results at about 300kbps, so you might have some luck.
I have a 4:20 long clip that...I'd like it to be...between 5 and 7 mbs.
Based on my own experience compressing for the web, I just don't think that will be possible with any acceptable quality.