There are area rugs in between these sizes. Also you can get any carpet bound in a custom size at a carpet store. Many have great remnants at low prices.

I am going to suggest, of the two sizes you are considering, the 5 x 7. And I am only choosing it because it will center with your furniture. 8 x 10 is too long.

Could we see a few more pictures of the room? You may be able to arrange the furniture differently. Hold off on a rug until you are sure everything is where it is supposed to be.

Do you like braided rugs? There are many 7x9 ovals that might work.

The seating will look more grounded if the rug slips under the front 1/3 of the sofas and extends past their ends by at least a foot or more. That would be the larger rug. You might do better to reverse the love and 3-seater locations. Do that and tape off again to see.

I see toys..lots of toys. They need a spot to go at the end of the day.

I, definitely, would suggest your rearrange the room and I would use IKEA for some extra pieces.

Use the interior long wall to house the tv, adding nice long stand , with lower drawers, for the toys. .Not hard to do and easy to add a few decorative pieces to give it some style.

Move the sofa under the large window and the love seat to where the t v is now. This arrangement lets you have an open entrance to the room.

You will have this effect, if you want to use a much larger rug…no need to go to great expense, either. What makes a rug look rich is a good felt pad and decent binding.