The Coalition Government's self-imposed rules mandate those figures to stay below 20 per cent and 30 per cent, respectively. This means Finance Minister Grant Robertson is $6.3 billion under his spending and borrowing limits.
Shaw said the Government should be using that money to invest in New Zealand's "massive infrastructure deficit".
"New Zealand's debt levels are well within what the international markets would deem to be prudent, interest rates are historically low and we have a massive infrastructure deficit; to me, that just all points in the direction of using that surplus for infrastructure investment in particular."
That investment, he said, should come from both the surplus and the 2.1 per cent headroom the Government has before it reaches its 30 per cent spending limit – a combined total of $11.5 billion.
"We often lose sight of why it is that we [MPs] do this stuff, which is to serve the people of New Zealand and make sure they have the basic services they need.
"A lot of New Zealanders don't have that right now and we have the ability to fix that for a lot of people – I just think we should."
Speaking to reporters at the release of the financial statements this morning, Robertson said it is important that Government had money set aside for a "rainy day", such as an economic shock.
He said the Government is already committing a lot of money into infrastructure investment – "$25 billion more than the previous Government," he said.
But he would not commit to using the surplus for infrastructure, or public health, spending.
And it's not just the Green Party lobbying the Government to spend its surplus.
The NZEI teachers' union said the Government's books show it has the room to "end the crisis in education today."
"The $5.5b surplus compares to an estimated $921m total annual cost of primary teachers' and principals' claims - including smaller class sizes, more support staff and a 16 per cent pay increase," NZEI President Lynda Stuart said.
She said the books show the Government "has the room to move if they have the political will to do so."
But Robertson said he believes the Government has already put a fair offer on the table for teachers.
"We have made an offer to teachers of half a billion dollars we think is appropriate. It is three times what was offered and accepted by teachers in the last nine years," he said.
National Leader Simon Bridges said the Government's surplus means it should not be imposing more taxes on New Zealanders already facing higher living costs.
"The Government has piled on taxes since the election. The extra fuel taxes alone are pushing up the price of petrol for Kiwi motorists by hundreds of dollars a year. It needs to reverse these extra costs."
