In Classic and Burning Crusade, 5-mans equaled difficulty of today's current Normal Mode raids. This is where casuals got better and eventually good enough to participate in raiding. Scholomance, Stratholme, UBRS, LBRS and even BRD were time consuming and challenging. The loot in these dungeons were valuable and second only to epics, epics mostly acquired via raiding. There existed rare questlines to obtain valuable epic gear outside of raiding, where the casual player could spend weeks collecting mats and running these dungeons in pursuit of a such a priceless commodity. Those days are gone and will likely never return, however I ask the community this:
What was wrong with 5-mans that taught players to become raiders? Why does it seem like the gap between the two has gotten bigger?
I don't mind hard 5 mans. I mind pugging hard 5 mans. This is where challenge mode. 5 guildies want to bash they heads for fun they can while other less geared people pug their normal 5 mans let them. LFR is meant to teach you to raid.
So there is no problem having a learning tier, it just goes on at other places: Leveling>Normal 5 mans if you are unlucky enough to not be h geared when you max> 5 h> LFR> N10/25>>H10/25 (H raids should be significantly harder).
The instances you have listed seemed harder because of two reasons:
1) They were more time consuming, which has nothing to do with difficulty
2) LFD has streamlined how players form 5-man groups, and as a result of that players gain much more exposure to the instances and as a result become better/more efficient at running the instances. Also, since players can run a higher volume of 5-man instances, they receive more gear and they receive it more quickly, therefore "over gearing" the content faster.
That being said, I don't think that 5-mans necessarily prepare a player for raiding (other than LFR "raids"). However, since players can gear up to the point of being eligible to participate in 5-mans much more easily, it makes them put forth the extra effort needed to bridge the gap between 5-mans and raiding.
From my experience, the only people that know what's going on in a LFR fight have 397 gear.
Also, LFR is to raiding experience as Baradin Hold is to raiding.