Spa tub vent critical distance

I am doing the DWV on a house I am building and can't figure the best way to vent the spa tub. The pic shows the main drain line in red and the proposed lav & tub line (2" ) in blue. My trap is more than 5 feet from the wall where I want the vent line and I know I can go horizontal with it below. Any ideas on how to vent this?

We would continue the line to the back wall, run the vent up there, and arm back to the "P" trap from that point.

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You have the right idea, but I would not run the pipes exactly the way you show them.