With a router or swtich and a pair of ordinary Ethernet cables, yes.  You can also use a crossover Ethernet cable - but not a single system to system straight-through cable.  This is assuming you plan to use the USB adapter on the newer system, which has no Ethernet jack, and the built-in Ethernet on the older system.    
Can I use the VisionTek USB-C to Ethernet 1Gbps Adapter (M/F) to connect a Studio 1537 and a Inspiron 15 5510/5518 using a regular ethernet cable to transfer files?
VisionTek USB-C to Ethernet 1Gbps Adapter (M/F) to connect a Studio 1537 and a 
Inspiron 15 5510/5518