Using fulltext search to find a sequence of digits
FTS is language specific; it can help you to find stuff in SQL Server which is specific to a language rather than treating it just like any other string in the databases. 

5088 is a base 10 number, I don’t think FTS will be of much help here. I think you’re only option is to use the LIKE operator. 

To learn more about why your query is running slow with like operator read Sargability: Why %string% Is Slow article by Brent Ozar.  



Alternatively, if you always look for a specific value in the column in question, you can make use of the Computed columns, something like... 

Test Table

CREATE TABLE #Test (ID INT , Value VARCHAR(100))
GO

INSERT INTO #Test VALUES (1 , 'ABC'), (2 , '') , (3 , 'EFG')
                       , (4 , 'A123BC'), (1 , 'AB123C') , (1 , 'ABC123') 
GO


Let's say you are only interested in the rows where it has a value of 123 and this the only value you always check for, then you can add another column (Computed) to the table, something like... 

ALTER TABLE #Test
ADD IsValid  AS (CASE WHEN Value LIKE '%123%' THEN 1 ELSE 0 END)
GO


And probably index the column too, something like....

CREATE INDEX NIX_IsValid_Record 
ON #Test (IsValid)


Now your query for records with 123 string should be... 

Select * from #Test Where isValid = 1


Even though you are looking for records with a string 123 anywhere in there but you will benefit from the Index on isValid column.