Stripes (awning to pin) or a plaid or a trellis pattern would coordinate well with your chair.

5x7 will probably be too small, the major seating pieces should have the front legs on the rug. You’ll want a lighter rug that is treated to resist stains and has a pattern that is small in scale. Since you are allowing the dogs access to it, you’ll want to get it cleaned periodically no matter what the color. I would bring in a color, like green, or you will have a gray/brown room and wonder why it feels blah.

Here are a few that would work with your pattern, you’ll have to decide on color and style.

rugs-direct.com amongst other rug sites allow you to upload a photo. You can then choose and see many rugs in your space.

So many blues in rugs. What you have is a denim blue, so a subtle pattern with that would work best with the bold pattern you have. It's too bad you didn't show us the rest of the room so that we could get a better idea of whether a rug like the one below works with your other furnishings. If you post in the future, please provide all four sides of a room and its adjoining spaces since good design is holistic--everything needs to relate.

Striped Blue Jeans and Cotton Rug, 8'x10' · More Info

With dogs and a door right there you may want to look at Flor.com….25% off now too

NitWit in chalk/silver might work….samples are only $2 and lots to consider:

Or Flor has a texture called Open Invitation that might work in the stone/mica color.

https://www.flor.com/area-rugs_carpet-tiles/graphics-and-patterns/open-invitation/21-1543.html

Flor carpet tiles are a great idea. Here's one on their opening page:

IMO something like this with no real pattern but all the colors from the chair

I would check Ruggable for washable Johnathan Adler rugs.