I'm not sure I follow, they both have a duration of 30 seconds and this duration is not affected by skillspeed or anything.

So, for example, if you hit the target with Lead Shot 2 seconds after you hit it with Hot Shot, exactly 30 seconds later Lead Shot will drop off 2 seconds after Hot Shot drops off - the timing gap between them doesn't change, and this gap is the same as when you applied them.

The only way there would be a 5 second gap is if you applied Hot Shot, waited a long time and then applied Lead Shot, or you refreshed Hot Shot early (in which case you'll be 'early' for Lead Shot by the same amount as well). It doesn't have anything to do with skill speed.