@BW4Equity  yes, but there are better options.  First, the D6000 is called a "universal" dock because it truly is universal.  The fact that it can connect to systems via USB-C or USB-A ("regular USB") means you can use it with anything, although using USB-A means the dock can't be used to charge the system.  But both the 3390 and 5300 have USB-C ports that support charging, so no worries there.  However, the D6000 uses DisplayLink technology, and that can have some significant drawbacks that I detailed in this thread, specifically the post marked as the answer.  The original question was about gaming, but my answer was much broader than that.

Unless one of the narrow use cases I described in that post for the D6000 apply to you, I would consider looking at a dock that taps into the system's native GPU outputs.  Since I wrote that post I linked above, Dell has released the WD19 and WD19TB to replace the WD15 and TB16, respectively.  Both of those tap into the native GPU outputs, and both will work with both of the systems you're asking about.  The WD19TB uses Thunderbolt, which it seems is available as an option on the 5300 but not on the 3390.  The WD19TB is actually backward-compatible with non-Thunderbolt systems, although only at reduced functionality equivalent to the regular WD19, so although it would work with the 3390, it won't offer any benefit over the WD19.  And although the 5300 could take full advantage of the WD19TB, if you have a display setup connected to the dock that requires Thunderbolt to use, then the 5300 will be able to use it properly, but the 3390 wouldn't.  So the only real reason to buy the WD19TB in your case would be if you wanted it for future-proofing in case you got another system that had Thunderbolt to replace the 3390.  Otherwise, if you want to have a display setup that will work with both the 3390 and 5300, you'll need a setup that works without Thunderbolt, in which case you might as well just get the regular WD19.

@jphughan Would the WD19TB support 3 monitors at 1440 (Dell U2719D)?  What about the WD19DC?  Or do I need to use the D6000?  I have an older XPS13 (9350) that has thunderbolt.  Thank you!

@kidkunithe WD19TB would support a triple QHD setup.  However, I don't know if it's actually compatible with the older XPS 13 9350.  It absolutely SHOULD be even though it isn't officially supported and listed as a compatible system, but Thunderbolt peripheral compatibility has proven to be a bit of a mixed bag.  That said, the fact that a given system doesn't appear on a compatibility list does NOT always mean that it's known NOT to be compatible; sometimes it just means that Dell never tested it, and in many such cases the accessory works perfectly fine with unlisted systems.  The WD19TB's predecessor the TB16 dock IS officially supported for that system and would also run triple QHD, but the TB16 itself has been the subject of a range of issues.  If I were you, I would get the WD19TB from a source that would allow an easy return if I had problems just in case, but I expect it would work.

The WD19DC is a dual connector dock.  It will only run triple QHD from systems that actually have two USB-C ports to run it.  Otherwise, although the dual connector can be separated to allow the dock to work with systems that only have a single USB-C connector, in that setup it works like a regular WD19, which will NOT support triple QHD.  The reason is that the WD19DC actually doesn't use Thunderbolt.  It uses two USB-C connections in order to achieve display setups that are typically only available via Thunderbolt -- but again that requires that it be connected to a system that actually has two USB-C outputs, which yours doesn't.  But the WD19DC is also only really meant for systems that require up to 210W of power (far more than can be carried over a single USB-C/TB3 connection), and the XPS 9350 only requires 45W, so unless you've also got something like a recent Precision 7000 Series model you want to use with the same dock, there's no point looking at the WD19DC.  And if you DO have a system like that, there's no single dock that will be ideal for both.  The DC is required for the extra power, but it doesn't use Thunderbolt to enable triple QHD on your XPS.  But the WD19TB wouldn't provide enough power.  In that case I'd suggest getting a WD19TB and planning to connect the Precision system's AC adapter directly to the system as well.  In theory the WD19DC's predecessor the TB18DC could have worked since it's dual connector AND supports Thunderbolt...but its dual connector doesn't support being separated, so it doesn't work with single connector systems at all.

@jphughan Thank you so much for the detailed and very helpful response!