SELECT FileID
FROM YourTable
WHERE ColourID IN (1,2,5)
GROUP BY FileID
HAVING COUNT(DISTINCT ColourID) = 3

-- You'll need to add this split function (Only run this part once).
-- Function is a modified version of:
-- http://weblogs.sqlteam.com/mladenp/archive/2007/05/22/60213.aspx
CREATE FUNCTION dbo.Split(@data VARCHAR(MAX), @delimiter VARCHAR(5))
RETURNS @t TABLE (data VARCHAR(MAX))
AS
BEGIN
    
    DECLARE @textXML XML;
    SELECT    @textXML = CAST('<d>' + REPLACE(@data, @delimiter, '</d><d>') + '</d>' AS XML);

    INSERT INTO @t(data)
    SELECT  T.split.value('.', 'nvarchar(max)') AS data
    FROM    @textXML.nodes('/d') T(split)
	    
    RETURN
END
GO


-- Start Creating dummy data
CREATE TABLE #FileColours (
	FileID INT, 
	ColourID INT
)

INSERT INTO #FileColours 
SELECT 1, 1
UNION ALL SELECT 1, 2
UNION ALL SELECT 1, 3
UNION ALL SELECT 1, 4
UNION ALL SELECT 2, 1
UNION ALL SELECT 2, 2
UNION ALL SELECT 3, 1
UNION ALL SELECT 3, 2
UNION ALL SELECT 4, 2
UNION ALL SELECT 4, 4
UNION ALL SELECT 5, 2
UNION ALL SELECT 5, 3
GO

-- Start query
DECLARE @Search VARCHAR(50) SET @Search = '4, 2'
DECLARE @Count INT
DECLARE @SearchTmp TABLE (ColourID INT)

INSERT INTO @SearchTmp 
SELECT CAST(Data AS INT)
FROM dbo.Split(@Search, ',')

-- Remember how many rows were populated
SET @Count = @@ROWCOUNT

SELECT FileID
FROM #FileColours f
INNER JOIN @SearchTmp t
	ON f.ColourID = t.ColourID
GROUP BY FileID
HAVING COUNT(*) = @Count
GO

-- Clean up.
DROP TABLE #FileColours 
GO