With less than 1Gb speeds, you'll not notice any improvement between a Cat5e cable, and a Cat6 or higher cable. Cat5e is rated for 1Gb speeds up to 325ft.
You'll get better mesh performance with a tri-band system, such as the TP-Link Deco X68 or similar. It has a dedicated WiFi band to move the traffic between the units.
Note that WiFi is all about location, location, location.
Keep your mesh units within 20, perhaps 25 linear feet of one another, and for best coverage radius, don't put them along exterior walls - keep them more towards the center of your home. This may mean running a longer cable between your modem, and your first Deco unit.