5e should be no issue. I am also using 5e to tarik cable from game room to my bed room.

What was the old model # ?
What is the new BTU model # ?

Check the termination. How is your cable terminated? Keystones or plugs?

The easiest way to go from 1000 to 100 is to terminate improperly.

5e should be no problem. check the termination.. most probably thats the culprit.. as suggested..
even cat 6 also will down to 100mbps if termination not good..

Colour pairs (T-568B) looks OK. Are the photos of both ends of the cable? If not, check the other end too, they should be the same. The plug is not clamped down on the cable sleeve so it's possible that some of the individual wires are loose and not contacting well or shorting its neighbour. I don't suppose you have a cable tester.

whoever done the crimping not pro ler.. crimp also not properly done.. 

That BTU looks like a different model than the HG8240H, could you take a picture of the underside? Should have sticker with model # there. EG8240H5 maybe?

latest modem will be this device for both unifi & maxis fibre

https://www.youtube.com/watch?v=QbaRDhpV3xI

ya lor.. looking at the crimped head.. if tugged hard the cable sure cabut at the connector there. the outer jacket should be crimped too inside the jack head.
that cable can be re-jack. just cut the current head off and crimped properly new jack.
if got IT friends can ask for help if he got crimper and head jack.