Search your own query, see the page at position 8, then open Search Console and see 5. The report is not correcting you, and you are not correcting the report. Those are two different measurements.
What the number actually averages
Google defines position as a relative rank, where 1 is the top result. The Performance report does not list every rank your links held. It shows the average of the topmost position your property or page occupied, across the queries where it appeared.
Google's example on that page: one query shows your property at positions 2, 4, and 6, and only 2 is counted. A second query shows it at 3, 5, and 9, and only 3 is counted. The average is (2 + 3) / 2 = 2.5. The lower links never enter the math.
Your search is not that average
Google states this in the same document. The report value is the average position for all searches. For your specific search, the position can differ because of your search history, your location, and other variables. A single query in a signed-in browser is one impression, not the average.
The chart and the Pages tab do not share one position
Chart totals are aggregated by property. The Pages table is aggregated by page. Google's counting rules say that if several URLs from your site appear for one query, the property records one impression and only the topmost position. Each URL is counted on its own.
Their worked example is three results from one property, in positions 1, 2, and 3. One person sees that page of results and clicks each link. Aggregated by property, average position is 1 and CTR is 100%. Aggregated by page, each URL averages to 2, because (1 + 2 + 3) / 3 = 2, and CTR is 33% per URL. A "better" position on the chart can be the same search as a worse position on the page row.
Unseen results are left out
A link has to earn an impression before a position is stored. If the result is on page 3 and the searcher never leaves page 1, that rank is not recorded. A dash in the report means there was no impression, so there is no position. Google's example is a page with 10 desktop impressions and none on mobile: desktop shows 10, and mobile shows a dash.
Position 11 is not one spot on the page
Google says the same number can describe different layouts. On a desktop web search, 11 might be the first result on page 2, if page 1 held 10 results and nothing on the side. It might also be a place in a knowledge panel, or a row of image results that is still on screen. The advice in the help page is to watch the change over time, especially sudden moves, and not to treat one absolute number as a simple rank.
How to read it next to clicks
Compare a stable date window, and read position beside impressions and clicks. Filter by device before you decide that mobile ranking moved. Use a manual search to see what you personally get. Do not file it as a correction of the average.