With most bettas being kept in small tanks, why compromise the health of a betta with a messy frog? I just believe these species should be housed separate. I don't think they gain anything from the pairing. And I do think you could expose the fish to pathogens it would not ordinarily encounter. Never kept frogs personally. Known people who have. I would rather see people keep another betta nearby, and let them interact visually through the tanks. I have always kept two to three males near each other on and off over many years. I think they benefit from the visual stimulation, unless it is an intense dislike, which happens on occasion. Mine have always enjoyed it, and most have lived long lives.
ADFs carry no pathogens almost ever that can infect a betta. Yes their bioload is a wee high but anyone wanting too keep aquatic animals healthy should have a filter and cycled their tank so this too should be a non issue.
Have I kept these together.. yep. However personal experience isn't enough to go on. Research is. I research every things I've ever kept in my 22 almost 23yrs in fish keeping.
I'll add though proper sized shrimp are the best suited for a 5g with a betta... btw they(betas) don't need friends. Thats a myth