I know this is a 7 year old thread, but the question was nearly identical and the accepted answer was what I started this with and eventually optimized to the following, which in my case returns consistently 85ms +-5ms with <some_column> being an indexed int field.
note1: the UNION ALL example in the accepted answer works too but was less performant in my case coming in at 300ms +-20ms.
note2: the next most upvoted answer (the row counter example) also works but was the least performant in my case coming in at 800ms +-70ms.
select
(select <some_column> from <some_table>
order by <some_field> limit 1) as oldest,
(select <some_column> from <some_table>
order by <some_field> desc limit 1) as newest
;
I did note that op referenced possible joins. I haven't had the need to include joins for my own purposes (just getting the current low and high IDs in fairly dynamic view) but with this model, the subqueries for oldest and newest should be able to be full fledged queries. Haven't tested, so not sure if it would work or be optimal.
I did test this model (which may also have already been suggested above) which might be a bit easier to join against, but the performance as-is was just a bit less than half of the example above, consistently returning 220ms +-10ms in my case.
select oldest.<some_field> as old,
newest.<some_field> as new
from
(select <some_column> from <some_table>
order by <some_field> limit 1) as oldest,
(select <some_column> from <some_table>
order by <some_field> desc limit 1) as newest
;