While I'm no expert, I don't know why it would only happen while moving. Assuming it is valve float, I'd guess that it isn't that you are moving, but rather under heavy load. Perhaps you don't notice it at light load?
While it is falling on it's face, since their is such light load you can't tell?
This was just my initial reaction to your post, perhaps I'm wrong. I don't see why the car would fall on its face at 5000 due to the trans. So I sorta ruled out the trans as a potential problem. AND since you just had valve springs put on, that seems to be where the main suspicion lies.
Who installed these? What valve springs are they? What is their installed height? How much seat pressure does your cam require? IMO- If you're not sure that they are installed to the correct seat pressure, then I'd suggest taking it easy until you are certain. If these were professionally installed, then perhaps it would ease your mind some, but if some buddy did it for you, then you better be finding out for sure before you destroy something.
While it's possible that swapping springs without checking the shims may provide the correct installed height, most likely it will not. I swapped AFR springs for some beehives and had to reshim a lot. The retainers and keepers sat at a different level on the valve than the AFR spring's retainer and keepers.
I used one of these to check the installed height:
http://store.summitracing.com/partd...CCA-4928&N=700+400114+304425+115&autoview=sku
Perhaps someone else can shed some light on this...
Rick