Modding a doorbell to a transceiver but need timer
As John1024 mentioned in a comment, the standard way to implement something like this is to use a 555 circuit, something like this:



Whenever the switch is closed, it will temporarily ground pin 2 of the 555, and the output on pin 3 will go high for the delay set by the components surrounding the 555.  If the delay needs to start on a positive going pulse instead, a transistor inverter can be added to the input side of the circuit.

The values for the 452K resistor connected to pins 6 and 7, and the 10 µF capacitor connected to pin 6, have been chosen to generate a time delay of 4.97 seconds which is the closest to 5 seconds you can get with standard components.

However the timing will actually only be as good as the tolerance of the capacitor, which can usually be no better than 5%.  So that means your timeout go range from about 4.7 seconds to 5.3 seconds, depending on the components.  (Of course for a given set of components, it will always be the same.)

The values for the two timing components were chosen using this online 555 monostable calculator.