I’ve heard Memphis St. fans claim for years they belong in the SEC. Maybe most of them have given up on that pipe-dream by now. However, they’re probably better in football over the past 3-4 years than they’ve ever been. They did get a Cotton Bowl bid a few years ago where they got clocked, but still they got the bid. Regardless, I don’t see them as P5 material. Somebody has to be at or near the top of the G5. That doesn’t make them P5. It’s about more than 1 or 2 seasons.
I think they’re decent in some women’s sports. Soccer comes to mind; they’re ranked 15th this week. So far this season they tied nationally ranked Ole Miss and beat Alabama, Indiana, Kansas and Iowa State.
The Memphis program is underfunded and doesn’t have P5 facilities. They have usually had decent to good municipal stadiums/arenas to use for football and basketball (although the stadium looks long-in-the-tooth).