This method works well if it is pretty good sized leak. 5-7 psi per week is probably more in the range of a medium sized leak, so it might be hard to spot by that method. Another way is to remove the tire, then set it down so it is perfectly flat (use a level, shim as required), inflate to normal tire pressure, then spray (or brush) some soapy water along the bead (where the tire rubber meets up with the metal rim). The soap will stay in the bead area and the leak will usually show up within 30 minutes, may be hard to see at first, often shows up as a bevy of very tiny bubbles. If no bubbles seen in an hour, flip the tire over and do the same to the other side’s bead.
I’ve had to remove tires from the rim a couple times to repair bead leaks. Once the tire is removed it is usually pretty obvious where the leak is, corrosion (rust, etc) easily seen on the bead in that area. A little sandpaper, emery cloth cleans it up straight away.