......A picture of your so called cat5e connector please?
Make sure the wiring at the connector can be seen clearly.

So this speed issue...
confirm inside properties that ur Ethernet is set to Auto Nego
confirm ur DIR-850L settings for LAN is 1Gbps

Lan cable does not really matter here... unless u going more then 10Gbps.

But the picture is WAN port....how about the other 4 LAN ports?

TS, issue solved already or not?

Take the path of least resistance, check the cable first. Use another one and see what happens.

Realtek is known to be picky with cables quality/length and gigabit. Try the problem cable with another PC/Laptop that doesn't use a Realtek LAN if you have any. If that works at gigabit, then you have to hunt for a different cable that works with your Realtek LAN.

Happened to me when I decide to wire my house with Gigabit, all non Realtek LAN (Intel/Qualcomm/KillerLAN) connect to my router at Gigabit. The two PC with Realtek LAN connect only at 100Mbps. All used the exact same cable

TS, issue solved already or not?

Go google how to change settings inside your network driver to gigabit, that's why you get 100Mbps instead of 1000Mbps.

That's interesting. What brand cables are you using? Strange that a network chipset can be affected by the brand of cables. What affects it? Aluminium, copper, resistance, impedance, conductance?

My 2 main computers are Realteks; Zotac Z77ITX, cheapo USB3 GBe for my MacBook. The MacBook is connected to a router using a Mediatek switch chip and the PC is connected to one using a Artheros switch chip.

This just made me realised that I don't know the brand of cables used in my house. Or I had forgotten. I must have specified something to the contractor. Must go check.