archmage and temporary spell slot

[With a box]

If a 17th level wizard (4 base 5th spell slots) borrows a epic ring of wizardry V(now 8 5th spell slots) and leveled up in archmage, and take spell like ablity a 9th. (now 7 5th spell/ or 6?)
and he returns the ring of wizardry to its owner.
now how many 5th spell slots he have?, 4? 3? 3.5?

and Can I use spell slots that gained by somthing else?
I think there is a artifact that me to cast at 18th sorcerer but limted to necromancy school (I can't find where it is....) with drawback of death of your lover.
Can I wear that and level up and use its spell slot to get High Arcana and throw it out of window?

[Nettlekid]

According to the text itself, you're using the spell slot to power the High Arcana class feature. If you lose the spell slot, you lose what's powering the High Arcana, so you lose access to the High Arcana. That's like asking "What if I have a lightbulb, buy a battery, hook it up so that the lightbulb lights up, and then return the battery. Do I get light for free?"

[atemu1234]

According to the text itself, you're using the spell slot to power the High Arcana class feature. If you lose the spell slot, you lose what's powering the High Arcana, so you lose access to the High Arcana. That's like asking "What if I have a lightbulb, buy a battery, hook it up so that the lightbulb lights up, and then return the battery. Do I get light for free?"

Note that if you've heard that metaphor before, you've worked in customer service.