Here's a pic I found online to kinda explain it:
1. Raise the seat to a height where when pedalling your leg is
almost fully straight.
2. On a bike that is the right size the top of the seat should be at about the same height as the top of the handlebars.
3. If you can't do both these things, then the bike is likely to small for you.
You mention having raised the seat 5 inches - that's a huge increase in seat height, if that still feels like it might not be tall enough it's almost certain that the source of your issues is that bike being far to small for you.
I suspect that bike being much to small for you is why getting on and off the bike is such a problem as well. Needing to be on your tiptoes to put your foot down when stopped is normal - normally when people come to a stop, they put all their weight on one foot, slide forward off the saddle so their waist is clear of the saddle on over the top tube, and put their other foot down on the ground as they stop. To get going again you do the opposite, put all your weight on one foot, use that to push yourself back up onto the saddle, then put the other foot back on the other pedal. I don't think that it's something you can avoid doing on a regular bike regardless of how low the bottom bracket it - the efficient point for your legs is being almost fully extended at the bottom of pedalling, and the pedals need to be a certain height so they don't hit the ground when you turn, so you're always going to need to get off the saddle to put your foot comfortably on the ground.
It's cool, a lot of us just wanted to get out there riding cheaply and ASAP. :-) You could also go to a bike shop. It's more expensive, but in addition to getting a new bike that's not partly worn out already, it also gives you the opportunity to ride several different size of the same model. A lot of shops also have a bike fitter that could take a look at you on the bike and tell you which size is the right size.
A decent hybrid bike from a bike shop (basically a mountain bike but without offroad stuff that's not needed, like shocks, knobby tires, etc) usually costs around $400 from a bike shop.