Declare new variable and input date based on rank - sql-server

Question

I want to 'clean' a dataset and declare a new variable, then input a date based on rank.
My dataset looks like this:
+-----+--------------+------------+-------+
| ID | Start_date | End_date | Rank |
+-----+--------------+------------+-------+
| a | May '16 | May '16 | 5 |
| a | Jun '16 | Jul '16 | 4 |
| a | Jul '16 | Aug '16 | 3 |
| a | Aug '16 | NULL '16 | 2 |
| a | Sept '16 | NULL '16 | 1 |
+-----+--------------+------------+-------+
I basically want to input the start date of rank 1 into the end date of rank 2 or say input start 5 into end 6 (always -1).
Have written the following to select into a tempory table and rank based on id and date:
SELECT
[Start_Date] as 'start'
,[End_Date] as 'end'
,[Code] as 'code'
,[ID] as 'id'
,rank() over (partition by [id] order by [Start_Date]) as 'rank'
INTO #1
FROM [Table]
ORDER BY [id]
Its the following part that doesn't work ...
DECLARE new_end
BEGIN select [#1].[start] into new_end FROM [#1]
WHERE (
([#1].[rank] = 1)
AND ([#1].[end] IS NULL)
)

Answer 1

Assuming you already have your dataset as provided in your question, this is just a simple self join, no?
declare #t table(ID nvarchar(1), Start_date date, End_date date, [Rank] int);
insert into #t values ('a','20170501','20170501',5),('a','20170601','20170701',4),('a','20170701','20170801',3),('a','20170801',NULL,2),('a','20170901',NULL,1);
select t1.ID
,t1.Start_date
,isnull(t1.End_date,t2.Start_date) as End_date
-- If you *always* want to overwrite the End_Date use this instead:
-- ,t2.Start_date as End_date
,t1.[Rank]
from #t t1
left join #t t2
on(t1.[Rank] = t2.[Rank]+1);
Output:
+----+------------+------------+------+
| ID | Start_date | End_date | Rank |
+----+------------+------------+------+
| a | 2017-05-01 | 2017-05-01 | 5 |
| a | 2017-06-01 | 2017-07-01 | 4 |
| a | 2017-07-01 | 2017-08-01 | 3 |
| a | 2017-08-01 | 2017-09-01 | 2 |
| a | 2017-09-01 | NULL | 1 |
+----+------------+------------+------+