When a character hits a target with a power that has an ongoing damage effect of 5 (for example psychic damage), and they have a feat which adds bonus damage of the same type of damage, does that apply to, or stack with the ongoing damage effect to make the target take extra ongoing damage?
Without seeing the exact text of the feat and power in question we can't say for sure, but it's unlikely that the feat will add its bonus to ongoing damage.
The key concept here is damage rolls. Almost everything that adds bonus damage adds it to damage rolls rather than to all damage. If you don't roll any dice for damage, it's not a damage roll (it's actually a little more complex as there are ways to roll dice for damage that don't count as damage rolls, but if you're not rolling any dice it's definitely not a damage roll).
Ongoing damage is almost always a flat amount: 5, 10, 20, etc. because it's a flat amount, there's no damage roll when the ongoing effect deals it's damage, and because there's no damage rolls anything that adds bonus damage to damage rolls will not add damage.