Lengthening a 5 ns pulse
A retriggerable monostable multivibrator such as 74LV123 would meet your requirements well: 


Minimum pulse width 3.0 ns for 3 volt operation, 2.5 ns at 5 volts.
Output pulse width configured by external R/C, typically 470 microseconds
Retrigger time 45 ns (3 volts) to 40 ns (5 volts).


It is a standard logic IC, very little complexity, and there are two monostables in the package in case you need to stretch another pulse source.

The part is available in DIP as well as TSSOP, so breadboard and production options.

Hope this helped.