Extending Ethernet to remote building 35m away

I need advice in designing a way to get internet access from one building to another 90 feet away and clear line of sight. I am able to use a catenary wire between the two buildings.
Present setup.
Main building
BT Hub3 2.4 GHz as the main router with a Belkin N600 DB wireless N+ router (Model F9K1102v1) as an AP connected via cat5 and situated in the loft at the other end of the building.

Proposed extension of Ethernet to other building 35 meters away.
My intention is to extend cat5 cable from the loft of the main building via catenary wire to the remote building as I cannot run another cable from the existing BT Hub5 Ethernet as all ports are now in use and in any case it is extremely difficult to run a cable within the building.
At the end of the existing cable I wish to use this cable to be able to use it connect an AP and extend the internet to the remote building. I do not know if this is possible with the use of RJ45 coupler F to F and Data-Data RJ45 Splitters or do I have to use other method?
Or would I need a Ethernet hub or switch.
See diagram below. Please note the two pcs’ are independent from each other not networked.

Would appreciate any advice on how to achieve extending internet from the BT Hub to the remote build with cat5e external cable. A sketch or diagram describing how to achieve it would be most helpful.
Thank you.

I would use cat6 never found spliters to work very well you need a router or switch which will give it a boost as well are you trying 100meg or 1000 meg. Its better underground in air it can be effected by frost & heat

Samuria said:

I would use cat6 never found spliters to work very well you need a router or switch which will give it a boost as well are you trying 100meg or 1000 meg. Its better underground in air it can be effected by frost & heat

I would use cat6

I can use Cat6 for external cable but I cannot change the already run cable which is cat5e, so having to connect a cat5e to cat6 may not be the thing to do.

need a router or switch

That is what I am asking but where has it got to be positioned and connected to?

are you trying 100meg or 1000 meg

This is for ADSL broadband not Gigabit.

Its better underground in air it can be effected by frost & heat

I'm afraid that is not possible, I would need to dig across a road!

Thank you,
You are the second person of a "few" whom I have asked that have suggested a simple and workable solution.

I have asked in other supposedly "network technical experts forums" and they all suggested complicated setups with antennae, and all sorts of different equipment to use which is why I then became very confused.

Like I said you are the second person suggesting the same simpler configuration.

Thank you.:)