According to industry analysts Barbour ABI, the figure represents an 8% increase compared to the same period in 2015.
Scotland was the top region for construction contract value in May, helped by the commissioning of the £1.3 billion Beatrice offshore wind farm in the Moray Firth.
Infrastructure performed strongly as well, leading all sectors with £2.9bn worth of contracts and 39% of the industry total. Commercial & retail also increased its monthly market value by 24% to £877 million.
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However, the residential sector's contract value decreased by 17% compared to April, while the number of units increased by 14%. Barbour ABI said this could be due to more 'affordable' homes being awarded within the month.
Michael Dall, lead economist at Barbour ABI, said: "With May figures hovering around the £6 billion mark, similar to the previous two months, this indicates a stable construction market that is looking towards the long term, with little sign of worry from today's EU referendum vote. However if Brexit does take place this is likely to cause a significant change in outlook at least in the short term with the likelihood of a reduction in activity.
"What is telling is the increase of contract values in May from the infrastructure and commercial & retail sectors, both traditional construction benchmarks that when performing well, give a solid indication that the industry as a whole is moving positively."
(LM)
