Bingenito has given the best answer so far but as he said you can always buy something better. (5 subs? Guess you then need integration)
Salk and Audio by Van Alstine electronics are always a very synergistic match, that is what I use with my Salk HT2-TL speakers. The combination of the AVA Fet Valve CFR preamp with the DVA SET 500 amp would leave enough in the budget for a couple pair of Hapa interconnects which are absolutely necessary to get the best sound. Read the Hapa reviews at their circle:
https://www.audiocircle.com/index.php?board=45I also use a HoloAudio DAC, none better for the price. The HoloAudio is a non-oversampling DAC, it doesn't have any digital harshness because is doesn't upsample (although it can internally with the push of a button but nobody uses it that way). The HoloAudio DAC's really shine when combined with a fairly high powered dedicated music server (not a laptop) with HQPlayer that runs state-of-the-art upsampling converting all music to DSD384. Then you will really hear what the Song3's are capable of.
I get lots of opportunities to listen to other brands of electronics through our local audio club and Van Alstine is still excellent sounding. A member uses a Luxman 509X integrated if you are itching to spend $10,000. It is a very nice sounding and good looking integrated. The Luxman is driving a pair of Joseph Audio Perspective2 Graphene speakers with a pair of Salk subs.
I have the Anthem AVM60 processor which I use for home theater, the preamp section pales in comparison to the Van Alstine Fet Valve CRF preamp which is clearer, tighter, less colored and more fun to listen to. The AVM60 is excellent for video and surround sound, which is totally different than stereo.
I use a single REL Gilbraltar G2 sub and never had a problem with integration. The sub has a LFE input so the Anthem does calibrate the bass for video. I use the recommended High Level Input (Neutrik Speakon) from the amp for stereo. REL subs are designed to be used with full range speakers like the Song3. I set my sub crossover at 32 HZ, right around where the HT2-TL rolls off (the Gibraltar has a digital display for crossover frequency and volume).
If I set the sub crossover at 50 Hz the sound would have "Dark mids, lots of bass bloom and loss of dynamics." Then I would need DSP like the Anthem to integrate and time align the bass. If music doesn't have bass material below 35 or 40 Hz I can't tell the sub is on. All music has 50 Hz content, that would effectively double the amount the amount of mid-bass by combining the Salk's with REL subs, that would be a disaster. REL subs are designed as sub-bass speakers although they can be used as plain old subs when paired with stand mounted speakers with limited low range.
There are a lot of set-up articles on the REL website:
https://rel.net/How to Fine-Tune a RELWhen you are dialing in your REL, stop focusing on what the clicks mean in terms of Hz steps, and instead focus on how it sounds in your room using your ears. Start with the crossover set a little low , perhaps bring it up a click or two, hear the sub and speaker marry up perfectly and then stop and enjoy. Learn to trust your ears. In the example using the speakers referenced above, you wouldn’t be crossing over at 28 Hz in any event because a REL needs to cross lower than the main speaker in order to blend perfectly. Have you tried the High Level Input Neutrik Speakon connection and lowering the crossover level to only enhance frequencies below 35 Hz? You may be pleasantly surprised.