Money is not tight and the wife and I do very decent for ourselves ... She just hates the fact its for entertainment and would rather it be used for better and more productive things in life.
Thanks for the clarification.
Most audio gear is pretty durable - good for 10 years or better. If you need to keep up with latest video, then the AVR has a shorter life. If you look at it that way, $5000 is $500/year or $1.37/day, or less than 2 packs of cigarettes/week (to give a comparison that might work to your favor). You can also put it in terms of trips to Starbucks.
The bottom line is to explain that it is a great source of joy in your life. She would be a rare woman if she is totally practical and doesn't have some form of indulgence for herself, be it shoes, mani/pedicures, etc.
A nice book to check out is "The 5 Love Languages" by Gary Chapman. While it is not at all specific to Audio gear, it does a great job of explaining how different people are attuned to different ways of communicating affection towards each other. The 5 "languages" are physical touch, quality time together, words of affirmation, acts of service, and gift giving. Life together is much easier if you know each other's language. My point is this book presents the idea of you placing different emphasis on different endeavors. You don't need to rationalize it, just explain that coming home and listening to music played on a high quality system just restores order to your chaotic day (or some such), and ask her to indulge you on this. Maybe present it as a mental health maintenance fee (not going crazy, but maintaining perspective, balance, and staying grounded) - that sounds pretty practical!
If she is practical in extreme, it is a safe bet that she really values you are passionate about some things. Audio is a manifestation of that!
Hope this helps and good luck!
Oh, and take her on a nice vacation!!!
Go exciting! A nice trip to some place like Costa Rica for a week including airfare is about the same cost as renting a condo on the US beach for a week (along with food and entertainment at beach).