I have lived in my Las Vegas home for more than 5 years without making any mortgage payments. Can I claim adverse possession?

No. Technically, you already own the house, and the bank only has a right of sale to satisfy the note. You cannot take "adverse possession" against yourself as the rightful owner. The bank is making those payments in order to protect their first-position lien interest, but because they've been making the tax payments along the way, that's another reason you can't take AP against them. No, you're going to have to pay the piper and either pay what's due or eventually lose the house to foreclosure. This is part of the deal you bargained for when you signed the mortgage, so you'll have to play it out.