I would guess you could get the RT-PCR test at any hospital. I know you can get it done at Chiangmai RAM hospital......3,500 baht (with results later in the day if you're tested in the morning or results the next morning if tested in the afternoon). I understand from reports that the cost at other hospitals can be as low as 2,700 baht.
If you arrived on a Monday, I'd think the following Friday is only 4 days away, not 5.