I'm sure there are loads of threads out there on this topic, just use the search function. Have you shopped around? NIB offer 2 year fixed at 4.20%, 3 year at 4.45% and 5 year at 4.90%. All below the quote you have mentioned. Their fixed rates top the best buys. You will have to be putting in some decent equity I would imagine, although if you are trading up I would expect that you have some equity to leverage up on.
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BoI have the best variable rate currently at around 3% for <50 LTV, but that's because they have not increased their rates at all in the last year, even with ECB increasing in April. Their rates are under review so don't be surprised if there is a big jump in the Variable to match the jump in their fixed rates