So I use this exact setup, with an even older / worse 13" MBP. I have the Late 2016 13" MBP dual-core i5, 16gb ram, 4TB3 ports version (the first one with the new design).
I've used it for 3.5 years now about 50/50 as a laptop and closed-clamshell into a 27" LG 4K (the UD68, the good bang-for-buck monitor that came out 3-4 years ago). During COVID and working from home for 5 months, that's more like 95/5 in closed clamshell.
I run it at "Looks like 2560 x 1440", understanding it's not true HiDPI pixel-doubling, which would need the 27" 5K. But honestly, it still looks great. Mac's scaling is pretty fantastic and I've been super impressed. The way I understand it works, they pixel double it pretending it's 5120 x 2880, and then downscale to the 3840 x 2160 4K monitor resolution. I run it at 60Hz refresh rate.
Overall I find it looks great. Rarely see any lag, tearing or any weird artifacts. That being said, I don't really use it for anything graphics intense. Now it's not perfectly smooth all the time, but my 6th gen Skylake is getting on in years too...
It may depend on what you would use it for and what monitor you get, but at least for me, I have been and continue to be really happy with the setup. Happy to discuss if you have any questions about it (here's how I'm setup. During the pandemic, working from home I've been basically sitting here 10hrs a day, 5 days a week, so really been using it a lot as of late).
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