Should I upgrade my Advent 5002 speakers?

The best speaker is the one you like! Keep the Advents as a secondary pair because resale value is low. What is your budget for new speakers? Do you prefer stand mounts or floor standers? How loud do you like to listen? Favorite music genre? How important is bass for you? How much space do you have for new speakers? There are a wide range of choices available for speakers!

Mr. Bourne is correct. I’d add that anything you buy is going to sound very different then the Advents, which were very good speakers, but age has definitely change their sound over the years and you’ve adjusted to them. I’m betting you’ll find most speakers will sound ‘bright’ to you. You’re best bet is try and listen to a number of speakers, and don’t mistake clean and clear for ‘bright’. The luxman amps are great. 

I think my dad may have a pair of these, I only know them as "Large Advents".  When I was home last I was impressed with their sound even though they are connected to less than ideal electronics.  You can always pick up a second pair of speakers, but think that the Advents are worth keeping.

You might try rebuilding the crossovers first , if you look up images of the 5002 you'll see that they are a simple design so upgrading the resistor , replacing and upgrading the 2 old worn out electrolytic capacitors ( electrolytics degrade over time and those are very old ) should make the speakers sound better than ever !   So for under $30.00 per speaker you can love your speakers even more .