Do you just have the HH5, or do you have the white Openreach modem as well?
Cannot see anything obvious there. Its a pity that the HH5 does not give error stats.
Can you hear any noise on your landline phone. Dial 17070 and select option 2.
To eliminate any issues with your wiring, can you connect things up as shown below, and see if things are any better.
Curiously, 99% of stuff, albeit a little slower then im used too are working now through Hotspot Shield, my normal VPN PIA still won't work though (note, i do not use a VPN all the time, just signed up to try and get somewhere with my Uni work.
Does this tell us anything!?