I think this will do what you need:
(note that it will probably get confused by overlapping ranges; don't know if they're possible in your data set)
select id, min(start_date) period_start, max(end_date) period_end
from
(
select
id, start_date, end_date,
max(contig) over (partition by id order by end_date) contiguous_group
from
(
select
id, start_date, end_date,
case
when lag(end_date) over (partition by id order by end_date) != start_date-1 or row_number() over (partition by id order by end_date)=1
then row_number() over (partition by id order by end_date) else null end contig
from t2
)
)
group by id, contiguous_group
order by id, period_start
/
Here's the test data that I used - based on yours with a couple extra entries:
create table t2 (id number, start_date date, end_date date);
insert into t2(id, start_date, end_date)values(5549, to_date('2008-05-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5567, to_date('2008-04-17', 'yyyy-mm-dd'), to_date('2008-04-30', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5567, to_date('2008-05-01', 'yyyy-mm-dd'), to_date('2008-07-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5567, to_date('2008-08-01', 'yyyy-mm-dd'), to_date('2008-08-14', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5567, to_date('2009-09-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5567, to_date('2008-11-17', 'yyyy-mm-dd'), to_date('2008-12-13', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5567, to_date('2008-12-14', 'yyyy-mm-dd'), to_date('2008-12-24', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5569, to_date('2008-05-01', 'yyyy-mm-dd'), to_date('2008-08-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5569, to_date('2008-09-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5589, to_date('2008-04-18', 'yyyy-mm-dd'), to_date('2008-04-30', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5589, to_date('2008-05-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5667, to_date('2008-05-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5828, to_date('2008-06-03', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(5867, to_date('2008-06-03', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(6167, to_date('2008-11-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(6207, to_date('2008-07-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(6228, to_date('2008-07-01', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
insert into t2(id, start_date, end_date)values(6267, to_date('2008-07-14', 'yyyy-mm-dd'), to_date('4712-12-31', 'yyyy-mm-dd'));
commit;