Well I called EVGA, said they couldn't get specs on the dimension 4700. So California Kid, I'm going to need you to measure inside your case to verify this card will fit.
He did however say that it is VERY rare for them to place RAM in a spot where the video card would be over it, he said it could be right up next to it but that it shouldn't hang over. Which it looks close in this case, I would say that it probably won't hang over. We have to remember that the thick part of the card is at the bottom or to the right if you are looking at the picture. So if his existing card (if extended) wouldn't hang over the RAM then we don't have to worry about it.
Ya, my guess is that the ram will hug the back of the card, and he might have to remove the video card to change the ram or something, nothing major though. This computer is probably from 2004, i bet back then they never expected video cards to be 10"+ long >.<