Why not fix for 3 years, overpay (assuming you can afford to, as you are used to paying at 5.79%) for this time then come the end of the term, you'll have a greater choice of products? I wont pretend to be a financial advisor, but the economy shows little sign of making a surge over the next year or so, so 3 years time maybe the sweet spot to give yourself the greatest % equity, then look at a longer fixed term from there in case of rising interest rates.
Its probably worth looking at what % equity you will have in the house in 3 years, and just get a rough idea of if this would make any significant difference to your payments. Base it on today's rates, do the maths then makes your choice