Gun safe or Gun Case

Ready to purchase my 5th pistol. I currently have a gun case that can hold all 5. Is that ok to use for proof of safe storage or do I actually need to purchase an actual safe? I also purchased about $500 worth of ammo online for home and range for my 4 other hand guns different calibers. Never spent so much...but making a good day at the range. Would I have problems with my background check at my FFL? I know NYC has no limit on ammo, but not looking to raise any flags just have a good day at the range with my guns and range friends.