Merge multiple rows into fewest number of rows of distinct values
Here are a couple ways you might approach the task by assigning an arbitrary row number to each of the non-NULL values for each column (avoiding extraneous sorts since the problem statement does not require ordered data) and then pivoting the resulting data into your final result set. 

Create test data

CREATE TABLE #table (
    ID INT NOT NULL,
    Col1 VARCHAR(100) NULL,
    Col2 VARCHAR(100) NULL,
    Col3 VARCHAR(100) NULL,
    Col4 VARCHAR(100) NULL,
    Col5 VARCHAR(100) NULL
)
GO
INSERT INTO #table (ID, Col1, Col2, Col3, Col4, Col5)
VALUES  (37850, '1A', NULL, '3A', NULL, '5A'),
        (37850, NULL, NULL, '3B', NULL, NULL),
        (37850, NULL, '2A', '3C', '4A', '5B'),
        (37850, NULL, NULL, NULL, NULL, NULL),
        (37850, NULL, NULL, NULL, NULL, '5C'),
        (37850, NULL, '2B', NULL, NULL, NULL),
        (37850, NULL, NULL, NULL, NULL, '5D'),
        (37850, NULL, NULL, NULL, NULL, NULL),
        (37850, NULL, NULL, NULL, '4B', '5E'),
        (37850, NULL, NULL, NULL, '4C', NULL),
        (37850, NULL, NULL, NULL, '4D', NULL)
GO
CREATE CLUSTERED INDEX CI ON #table (ID)
GO


Perform the desired merge and flatten with one scan of the data per column and only a single sort (or hash group) on the final set of rows

SELECT ID,
        -- Pivot the data for each ID / row number pair,
        MIN(CASE WHEN colNumber = 1 THEN val END) AS Col1,
        MIN(CASE WHEN colNumber = 2 THEN val END) AS Col2,
        MIN(CASE WHEN colNumber = 3 THEN val END) AS Col3,
        MIN(CASE WHEN colNumber = 4 THEN val END) AS Col4,
        MIN(CASE WHEN colNumber = 5 THEN val END) AS Col5
FROM (
    -- Within each ID, assign an arbitrary row number to each non-NULL column value
    SELECT ID, ROW_NUMBER() OVER (PARTITION BY ID ORDER BY (SELECT 0) ASC) AS rowNum, 1 AS colNumber, Col1 AS val FROM #table WHERE Col1 IS NOT NULL UNION ALL
    SELECT ID, ROW_NUMBER() OVER (PARTITION BY ID ORDER BY (SELECT 0) ASC) AS rowNum, 2 AS colNumber, Col2 AS val FROM #table WHERE Col2 IS NOT NULL UNION ALL
    SELECT ID, ROW_NUMBER() OVER (PARTITION BY ID ORDER BY (SELECT 0) ASC) AS rowNum, 3 AS colNumber, Col3 AS val FROM #table WHERE Col3 IS NOT NULL UNION ALL
    SELECT ID, ROW_NUMBER() OVER (PARTITION BY ID ORDER BY (SELECT 0) ASC) AS rowNum, 4 AS colNumber, Col4 AS val FROM #table WHERE Col4 IS NOT NULL UNION ALL
    SELECT ID, ROW_NUMBER() OVER (PARTITION BY ID ORDER BY (SELECT 0) ASC) AS rowNum, 5 AS colNumber, Col5 AS val FROM #table WHERE Col5 IS NOT NULL
) x
GROUP BY ID, rowNum
GO


In SQL Server 2017+, perform the desired merge and flatten with a single scan over the data and no sorting

SELECT s.ID,
    -- Pivot the data for each ID / row number pair,
    MIN(CASE WHEN v.colNum = 1 THEN v.value END) AS Col1,
    MIN(CASE WHEN v.colNum = 2 THEN v.value END) AS Col2,
    MIN(CASE WHEN v.colNum = 3 THEN v.value END) AS Col3,
    MIN(CASE WHEN v.colNum = 4 THEN v.value END) AS Col4,
    MIN(CASE WHEN v.colNum = 5 THEN v.value END) AS Col5
FROM (
    -- For each ID, build the list of non-NULL values, using
    -- a delimiter that will not exist in your data
    SELECT t.ID,
        STRING_AGG(t.Col1,CHAR(0)) as stringAgg1,
        STRING_AGG(t.Col2,CHAR(0)) as stringAgg2,
        STRING_AGG(t.Col3,CHAR(0)) as stringAgg3,
        STRING_AGG(t.Col4,CHAR(0)) as stringAgg4,
        STRING_AGG(t.Col5,CHAR(0)) as stringAgg5
    FROM #table t
    GROUP BY t.ID
) s
OUTER APPLY (
    -- For each ID, unpivot the list of non-NULL values,
    -- appending an arbitrary row number to each value
    SELECT value, 1 AS colNum, ROW_NUMBER() OVER (ORDER BY (SELECT 0)) AS rn FROM STRING_SPLIT(s.stringAgg1,CHAR(0)) UNION ALL
    SELECT value, 2 AS colNum, ROW_NUMBER() OVER (ORDER BY (SELECT 0)) AS rn FROM STRING_SPLIT(s.stringAgg2,CHAR(0)) UNION ALL
    SELECT value, 3 AS colNum, ROW_NUMBER() OVER (ORDER BY (SELECT 0)) AS rn FROM STRING_SPLIT(s.stringAgg3,CHAR(0)) UNION ALL
    SELECT value, 4 AS colNum, ROW_NUMBER() OVER (ORDER BY (SELECT 0)) AS rn FROM STRING_SPLIT(s.stringAgg4,CHAR(0)) UNION ALL
    SELECT value, 5 AS colNum, ROW_NUMBER() OVER (ORDER BY (SELECT 0)) AS rn FROM STRING_SPLIT(s.stringAgg5,CHAR(0))
) v
-- For each ID, group together all column values with same row number
GROUP BY s.ID, v.rn
GO


Visualize the test data



Visualize the results