I am trying to look farther down the runway like my instructor has advised. I think maybe I'm not understanding WHAT the plane is supposed to do during this 5 second period. Is the idea that the initial roundout is to simply level the plane off and hold it there, waiting for the ground effect to go away? And then as all that goes away, start pulling back more for the flare? I mean, I've watched a million landings before but the feel of it from the cockpit is proving to be sort of counter-intuitive...
A few things to consider:
As Bob wrote, ground effect doesn't "go away" as you slow down but that's not anything you need to be concerned about now. What does "go away" (i.e. diminish as you slow down) is the effectiveness of the controls, especially the elevator. Compounding that is the fact that you need to raise the nose higher and higher as you slow down to maintain lift (prior to stalling of course). So a proper roundout and touchdown requires that you gradually but continually pull the wheel or stick back further and further until you touch down. In the ideal case you will have the wheel nearly or completely all the way back at the same point in time that your wheels are a half inch above the pavement but that's not necessary or realistic when just learning to land. The key point is you cannot stop moving the elevator even though that's almost always exactly what your instincts are telling you to do.
As to looking way down the runway and what you're trying to see then, watching the distant horizon makes it much easier to sense how fast you are sinking and how high the airplane's nose is. Like I mentioned your pitch attitude should be increasing, at least until you clearly have the nosewheel higher than the mains (touching down nose first can cause serious problems). If you have power available you don't have to raise it any higher than that if you use power to control the descent rate at that point but this is an "improper" technique that won't work when you need to make a power off landing so I'd try to avoid it if you can. As long as you are above stall speed you can and should control the descent rate by adjusting pitch with the elevator. Your goal should be to reduce the sink rate gradually as your height above the runway decreases from a few feet to a few inches or less. That exercise someone suggested where you fly down the runway at low speed without trying to touch down is a good way to learn how to sense sink rate while looking far ahead.
BTW looking at the far end actually makes it more difficult to judge the distance between your wheels and the runway so what I find works best is to switch your focus back and forth between the far end and about 20-30 feet ahead. That way you get the ability to see the sink rate and your height.
Finally I want to relate a problem I had when learning to land. For some reason I had a strong subconscious desire to touch down with the wings level and no one ever explained that this is neither necessary nor desired if there's any crosswind. I think I had some kind of fear that if one main wheel touched before the other the plane would veer off the runway but in reality there's no such effect. This is really a crosswind issue but unless the wind is calm there's almost always at least a slight crosswind component which will cause the plane to drift toward one side of the runway if you don't correct for it. And the only correction that works is to lower the wing into the crosswind while using the rudder to keep the plane aligned. In light winds you don't have to think about which wing to hold lower, just "steer" the airplane with the ailerons and keep the plane in the center without worrying about how level the wings are. If the plane stays in the middle and you keep it pointed down the runway you've got the right bank angle.
Bruce Chien has often posted his "butt sink" method for the roundout and touchdown and it goes something like this:
Maintain pitch attitude and airspeed down your approach until you've passed the threshold and are about 10-20 feet above the runway.
Start raising the nose until it feels like your butt isn't sinking anymore. With a little luck you'll be no more than a few feet above the runway at that point.
Hold that pitch attitude until you feel your butt sink some more and then stop the sinking or at least slow it down to almost nothing.
Repeat that until your wheels touch. Each time you sense you are sinking pull back a little to arrest the sink and the result will be that you will have very little vertical speed when you touch down.
In reality, much of your sense of "butt sinking" should come from watching the far end of the runway (actually the far horizon but the difference is minimal in a 172 on a 2500+ ft runway). But if you stare at the far horizon you will have little idea of how high you are and the touch down is likely to occur earlier or later than you might expect.
The rest of the landing technique involves keeping the plane in the center of the runway with the ailerons and pointed down (aligned with) the runway using the rudder pedals. At first this feels like rubbing your tummy with one hand while patting your head with the other but eventually most of it becomes "muscle memory" leaving your cognitive bandwith for more of a supervisory function.
