We present a catalogue of nearly 3,000 submillimetre sources detected at 850um over ~5 square degrees surveyed as part of the James Clerk Maxwell Telescope (JCMT) SCUBA-2 Cosmology Legacy Survey (S2CLS). This is the largest survey of its kind at 850um, probing a meaningful cosmic volume at the peak of star formation activity and increasing the sample size of submillimetre galaxies selected at 850um by an order of magnitude. We describe the wide 850um survey component of S2CLS, which covers the key extragalactic survey fields: UKIDSS-UDS, COSMOS, Akari-NEP, Extended Groth Strip, Lockman Hole North, SSA22 and GOODS-North. The average 1-sigma depth of S2CLS is 1.2 mJy/beam, approaching the SCUBA-2 850um confusion limit, which we determine to be ~0.8 mJy/beam. We measure the single dish 850um number counts to unprecedented accuracy, reducing the Poisson errors on the differential counts to approximately 4% at S_850~3mJy. With several independent fields, we investigate field-to-field variance, finding that the number counts on 0.5-1 degree scales are generally within 50% of the S2CLS mean for S_850>3mJy, with scatter consistent with the Poisson and estimated cosmic variance uncertainties, although there is a marginal (2-sigma) density enhancement in the GOODS-North field. The observed number counts are in reasonable agreement with recent phenomenological and semi-analytic models. Finally, the large solid angle of S2CLS allows us to measure the bright-end counts: at S_850>10mJy there are approximately ten sources per square degree, and we detect the distinctive up-turn in the number counts indicative of the detection of local sources of 850um emission and strongly lensed high-redshift galaxies. Here we describe the data collection and reduction procedures and present calibrated maps and a catalogue of sources; these are made publicly available.
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