It's unclear from your description what you feel your options are. But if you're adding two bedrooms, you should probably add a shared bathroom for them.

The existing slope of the terrain does not favor adding on to the house unless you truly need (and can afford) using the lower level for non-habitable space, i.e., for cars, storage, etc.

Call a local architect. A lot will depend on the existing layout of the house and how the added bedrooms best relate to the other spaces.

I feel my options are to build an addition on the side where the red is- and use the below space as just a carport. Or to raise the roof and build more bedrooms on the second level.

Working with an architect will save you money on a project such as this. Since you mentioned you are buying this home have you checked that additional bedrooms will be allowed? I know some areas the infrastructure will not allow for more bedrooms and bathrooms or if allowed the sewer and such must be improved which is a large cost.

Buy the bigger house that costs double this one, that you really want. In the end, it will cost less.

^^^^^^ THIS!!!

I guess the issue is I've been searching for a house for a year and everything is so overpriced right now and everything sells fast in my area (people are buying without even seeing the homes) and I have the opportunity to buy this house super cheap on 5 acres and anything with acreage around here is VERY expensive.

I don't think building it over the driveway there will work unless you rework the driveway approach as well as it seems you will be driving into the carport at a slope.

You might be able to do it on the other side with either a crawlspace to extend it out or you could bring it out into the front and create an L-shape, however this is without knowing what the other side looks like or what the interior looks like, but I'm thinking at least with 5 acres you won't be near the set-backs.

Having to upgrade a septic is likely needed if you are adding bedroom, but if you're on sewer then it shouldn't be an issue. For the septic if it is in good working order it is likely you can just add onto it. This was done at my old house when the previous owner made an addition.

Why can't you extend off the other end of the home?

The reason I cant build off the other side of the house is because that is where the well and septic tank are. :( I would love to just build new on this land but the whole 5 acres is on the side of a mountain so it slopes down.

Are the well/septic in front of the house on the right?

"buy this house super cheap on 5 acres and anything with acreage around here is VERY expensive."

Perhaps that's why if your options to do most anything are that limited.

I'm buying it from a family member- that's why it's so cheap- and it needs lots of updating which I have no problem DIYing the cosmetic stuff.

The septic/well are directly next to the house on the other side unfortunately.

So two car tuck under garage? Change THAT space into the living space you need now with walkout lower level. Go without a garage until you can afford to build a freestanding one on that acreage.

So you could still do an L shape house with the addition on the front right side, not next to the house, but in the front? You might need a retaining wall from the slope, but it looks fairly flat there from the pictures you posted.

Yes an L shape could possibly work- that is where the living room is so it may be an awkward layout too but that's what we're working with.

I think worst case scenario if the additions arent reasonable or possible- we just fix it up, finish the lower level, and sell it and use the profit to be able to afford a bigger house.