Update (5/10/2012) -- After releasing Troy Woolfolk and signing Ben Bass and Jamize Olawale, we are $2,044,361 under the cap. Neither Bass nor Olawale got a signing bonus.
Also, our reported rookie pool of $5,714,522 DOES NOT include the undrafted rookie reservation of $25,528, it's only the pool for the draft picks. Therefore, our total rookie pool is $5,740,050. If we use every dollar for our draft picks, signing them will use up $2,684,522 of cap room. As I stated before, almost all of this will come from signing Claiborne. Signing our other six picks will have very little effect on the salary cap, because of the Top 51 Rule.
All of this means that after Newman's release becomes official and we sign all of our draft picks, we should have about $4,910,839 of cap room left if everything else remains the same.