Yeah. Unfortunately you probably wouldn't get past the automatic gates trying to get into T3. Alternatively, if you wanted to exit T5 and go over to the T2/3 area you could buy a day pass for one of the arrivals lounges over there which are located outside security. I know AA has one which is $90 for those traveling in cabins other than J or F and who don't have Emerald status. There's also a Plaza Premium arrivals lounge in T2 which may be a bit cheaper. It may be worth a bite to eat and a nice shower in between flights. I'm not sure which others may sell day passes, but there are quite a few over there.