Looking at the HH5 stats it appears that 13mb is the most you line can support. You'dve been better staying on ADSL2.
You can't get FTTC on an exchange-only line - because there isn't a cabinet. Sometimes they will install a new cabinet just outside the exchange, though.
It sounds like you're a long way from the cabinet. The VDSL2 signal used by Infinity doesn't travel so well as traditional ADSL (or ADSL2+), so on a long line, there may be no improvement in switching to it.