Heater on 1990 Toyota Camry mysteriously quits working after about 5 minutes of operation. I have checked the blower motor and the switch and they work fine.

Sounds like a bad heater switch.
Maybe loose wire that feeds the heater motor.
OR the blower resistors is making and breaking the circuit.
Possible bad heater motor. Try smacking the lower right dash panel when the heater is is in the "ON" position.

Find the heater motor first.TAP on the motor-if it goes then ,the heater motor is most likely faulty with burned brushes,inside.

its behind the glove box and a little to the left

It is located behind the glove compartment, which you have to remove, see p35 here

http://www.turboninjas.com/camry/ac.pdf

There is a resistor pack that is in the heater box next to the blower motor, this is what gives the different blower speeds. They some-times burn-out cutting off the power.

Your blower fan is most likely failing. It sounds like it is rubbing on the cage, which causes the motor to heat up and quit functioning. Once the motor cools down it will operate again. You will need to replace the blower motor and fan assembly.

not sure where but i am positive that its a ground problem. if you add a ground to the blower motor i am sure that it will work and might even get others back as well. or you can check all your groundsu

The switch or resistors at the blower motor.( resistors are usually found next to blower motor)
Ther relay is the last place you check for resistance. However, before doing any kind of electrical testing or repair POINT THE WHEELS STRAIGHT AHEAD. DISCONNECT THE NEGATIVE BATTERY TERMINAL. WAITE AT LEAST 2 MINUTES FOR BACK UP POWER SUPPLY TO BE DEPLEATED..THEN DISCONNECT THE YELLOWAIR BAG CONNECTOR LOCATED UNDER THE STEERING COLUMN NEAR THECOMBO SWITCH AND BEHIND THE GLOVE BOX FOR THE PASSENGER SIDE AIR BAG. BE CAREFUL AND GOOD LUCK

There could be some electrical connections lose somewhere in the ac/ blower fan circuit, worth checking it.

heater fan speed switch located in heater box by passengers feet up in heater box one plug on it cant miss two screws hold it in!!!!