How to delay a relay closing?
simulate this circuit &ndash; Schematic created using CircuitLab

A CMOS schmitt trigger 40106 or 4093 (check the numbers) would work for this.


Pick a reasonable value for C1 - 10uF, say.
Calculate R so that R * C = 5 s.
When the input goes high C1 will charge up. At about 2/3 of supply voltage NOT1 output will switch low and NOT2 will switch high. Q1 will turn on and the relay will pull in.
D1 allows instant reset by discharging C1 when input goes low. It may need addition of a resistor to limit the current to whatever's driving the circuit.
D2 protects Q1 when RLY1 is switched off.