Propagation delay signal time
Assuming a '6 nS signal' means a pulse of length 6 nS, and assuming that the 5 nS delay applies to both the high-going and low-going edges for the gate, then the 6 nS pulse emerges from the gate output as a 6 nS pulse, 5 nS after it went in.
In general, gates tend to have different specifications for the tPHL and tPLH times (time for Propagation High to Low, and vice versa). As a result, the pulse will be stretched or compressed by the difference between these times. This is generally known as Pulse Length Distortion. Note that for a short enough pulse, and a large enough difference between these propagation times, the pulse could disappear.