Is it normal to still be grieving terribly 5 years after someone died?

I think that depends from person to person, situation to situation. A particularly traumatic or sudden death can take years to heal from, and we all handle the grieving process differently. May I suggest you read Elisabeth Kübler-Ross' "On Death and dying," and her "The twelve stages of grief." Both books have been very helpful to me, and others that have read them. And, you may want to seek bereavement counseling from a local hospice. Dying and death are what they deal with, so who best to help?