To get sensible answers to your question, as with all design you must decide exactly what it is you want to achieve. Having decided on the requirements the next question should be "make or buy?" - don't bother making it if you can already buy something that does the job, such as a time delay relay.
If you must design a circuit, for us to give answers you need to provide specific information such as:
1)What exactly is the "input signal"?
2)What is it required to do at the receivers? Does it need relay contacts to control the receiver, for example to turn on the power, turn off the squelch or muting circuit, or what?
3)How accurate does the 5 second delay need to be?
4)What power supplies are available to run the delay circuit?
5)What temperature range must it work over?
6)Shielding EMC considerations - are there any high power transmitters nearby?
7)Size, weight, cost?