do you have to roll a saving throw for each five foot square that you enter 

It's a shame they didn't fix this spell... it's still broken. If you cast it on a flying creature, like a dragon for instance, then the target (dragon) is restrained and falls right out of the sky. Wham! Instant falling damage from a 2nd level spell... since the range is 60 ft, that's only 6d6 if the caster is on the ground and the target is flying, but if you are both flying very high up, you could inflict up to 20d6 with a 2nd-level spell. ... not to mention, this spell makes the Earthbind spell much less useful, since it's entire purpose is to pull down flying creatures, but it does so without causing damage. 

And the dragon can't spend an action to break free or make a saving throw till the beginning of its next turn, but falling happens instantly to any creature that is restrained. Yeah, the web spell isn't anchored so it will disappear at the start of your next turn, but by the time your next turn rolls around, whatever flying creature you caught with the spell is already dead (or badly hurt, with an average of 70 damage from a 200 ft fall). 

Am I misreading something here? 

Quote from DrailenVincere >>

do you have to roll a saving throw for each five foot square that you enter 

 No. You only make the save the first time you enter the webs, or start your turn there. If you make the save, you treat the webs as difficult terrain and can try to get out of them before your turn expires. Since it's only a 20 ft cube, you should be close enough to one of the edges to get out in one turn even with half-movement speed. 

Web is cast on a point in space, it isn't cast on the creature therefore it doesn't follow the creature. Imagine, if you will, a cube of webs appearing in a point in space. The spell collapses as fast as the webs are filling the space meaning that for 1 turn (because it isn't anchored) there is a mass of webs within that cube dictated by the point in space you selected. On your turn, nothing happens - the creature isn't entering the spells area (the spell was cast in the area the creature is in) and it is still your turn.

On the creature's turn, it is indeed within the web cube, and since you haven't had a second turn, the cube persists. The dragon would therefore need to pass a dexterity saving throw against your Spell DC or become restrained. Assuming they fail this save with no legendary resistance to force a success, then they would indeed be restrained. However, at this point they would begin falling and they would fall out of the spells area (outside of the cube, falling down towards the ground). Once they exit the space of the spell the next condition triggers, meaning it is no longer restrained because it is no longer in the area of the spell.

So all a web spell would do, if not anchored, would force a dragon to fall 20 feet at most through the area of the spell and then regain the ability to fly - a minor inconvenience.

There's one corner case which would require DM adjudication, where a friend acts between you and the dragon. You summon the webs, they grapple or push the dragon into the webs triggering the "enters the web on a turn". The same restrained condition would apply, but then would be removed when it fell outside the area of the spell, but then it is your friend's turn and not the dragon's, so it may not get a move action to correct the "fall" and ipso facto hit the ground - although I think most DMs would just say the dragon rights itself - unless it made for a good story!