Mark - what are you trying to accomplish? Are you looking from a habitat perspective or a timber value perspective?
With 5 acres you are going to really struggle to find someone interested in logging if that is what you are thinking. I can't speak for the pines, but the beech, hickories, sycamore and gum trees are low grade timber (at least in my area). Even the large oaks will be a hard sell simply because I would venture to guess you don't have many of them. Logging is all about volume and moving that equipment is expensive.
From a habitat perspective - you may be caught in a catch-22 regarding the oaks. I will say that any of the younger oaks that appear to be near ready to produce I would release from any beech, gum, sycamore or hickory in a heartbeat. As for the cases where that young oak is fighting with a mature one - you have to make that decision. In some cases you may decide the large one needs to go to release the younger ones, and in others you may want the mature tree to stay. I would NOT cut ANY of the younger oaks unless absolutely needed. As for the other trees. The beech, hickory, gum and sycamore - these are of relative little use to the deer once they exceed the deer reach. The largest of these I would consider removing simply to produce a thicker understory. Beech produce beech nuts that the deer will eat and provide some nice stand trees because how they hold their leaves, but again - you have to decide if it provides enough value or not. I know sycamore stump sprout well and I think gum does as well. Hickory tends to hinge well if that interests you.