Modern conventional goes 5k. Synthetic has been shown to go much, much longer. At 7k, full synthetic should still have life to it.
3k is a myth. Some states are considering publishing data about it. The quick oil change industry has done a dang good job telling everyone more is better and it is a huge, huge, huge waste.
If you go full synthetic, you will be fine at 5k and honestly, 7500. Unless your engine is running bad, your oil should be fine. If your engine runs rich, lean or has some weak seals and allows more blow by gases into the oil you will be fine at 7500.
If you move to synthetic, you can do a 5k first time around and have the oil evaluated by one of the many companies that do it. They will tell you how your engine is wearing.