I dont think that what you have or what I have is a "collection", and I dont think they are "sporting goods" either, and I dont think the $5000 limit cuts it.
I have "replacement value on my contents". I pay extra for that. I would expect them to ask me to prove that I had what I say I had and then I would expect them to replace it once I proved it.
The best advice I ever got was from a friend who had a fire. Long story short, place burned down, buddy had a video from a party at his house and the Ins. Co. replaced everything clearly seen in the video.
Bottom line - every couple years walk around your house with video camera, open the closets, open the drawers, etc etc and provide some commentary - there are 12 pair jeans here, 4 suits, my wife has 20 pair shoes, this Browning OU is worht $4K, etc. Makes claims go a lot easier (keep the video on a flash drive in your safety deposit box).
They place limits on some things and they are spelled out in the policy - like coin collections, cash, jewellry, fur coats, etc, because it is pretty easy to say "I had $50K in $20's in the basement and now they are gone"...prove it...well I can't.