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 .

Should have mentioned that the crossovers have been rebuilt already, but always good advice for older speakers.

@jasonbourne52 I really do like the Advents, but guess I’m just wondering if they’re a weak link in my system.  My listening is mostly jazz and rock, with a little classical thrown in from time to time.  Bass is only important in so far as the can accurately reproduce it, but I don’t want it thumping when it shouldn’t be.  I’d like to keep the size pretty close to the Advents and the price under $4000.  I’m more concerned with accurate than loud.  The MoFi speakers seem to fill both of those desires, but they’re still pretty new so there’s not a ton of info on them yet but what there is is glowing.  

How about this: the speakers that impressed me the most over the past several years have been the Ohm Walsh Sound Cylinders! I bought a seond-hand pair quite cheaply. They may be the best sounding and better than any of the other speakers in my collection! And this includes my Quad 57's! Stunning 3 - D room-filling sound from any spot! The performers are right there in the room! I am impressed! Ohm Acoustics in Brooklyn, NY can probably build you a pair of Sound Cylinders in the finish of your choice. You can contact and speak to the owner John Strohbeen. Ohm has been established over 40 years!

Except for the size part, it sound like you might like Vandersteens.

Stand mounts...if it were me I'd go with MA Silver 100s. But that's just my personal taste.

Second the motion on checking out Ohms. I have a pair of 1000s and they are great. Ohm also has a 120 home trial period, so you can return them if they don't pan out for you. You are just out shipping. 

Should I upgrade my Advent 5002 speakers?

Yes, you should.

I am a huge fan of the Large Advent. Henry Kloss worked some magical engineering into the voicing that still amazes people today. That said they are not the last word in definition and dynamics. Time moves on. Footprint and architecture-wise the SourcePoint 10s bear more than a little resemblance to the Advent, from the 2 Ft3 box to the 10-ish inch woofer and slightly oversized tweeter to enable a lower crossover point. All straight from the Advent playbook. I have admired Mr. Jones work for a long time, and he doesn't do sloppy work.. But, there is another speaker i would seriously consider: the Monitor Audio Silver 500 7G. There are several reasons why Stereophile put this on their Class A list, at a price about 10-20% of most of its peers.  It is really, really good overall. It is accurate, dynamic, has great bass extension, is pretty easy to drive, and is simply provides a listening experience to which you want to return - often. Although a tower, it takes up no more room than the SourcePoints on their obligatory stands.

Rather than repeat what others have said, for both speakers, read the reviews, and find a pair to audition. 

I believe that there ar 2 caps, 2 coils and 1 resistor in the 5002's.  Replace the 7uf and the 32uf electrolytic with a decent mkp (polypropylene).... Even cheap mkp will be an audible improvement over the 40 year old electrolytic. I believe the resistor is a 3 ohm wire wound.  Grab a 10 to 15 watt non or low inductive resistor and replace that also while you are at it.  It won't make as much of a difference as the caps, but on decent equipment, is still audible.  Leave the inductors (coils).  After you do this inexpensive upgrade, then make the decision to replace or not. I hope this helps,  Tim