Order by lowest value of one column grouped by another column

Question

This was really difficult to explain in the title of this, but here is a table that I have:

CATEGORY_ID   COUNT   GROUPING
1             130     H
2              54     B
3             128     C
4              70     D
5              31     E
6              25     F
7              64     A
8              59     F
9              66     B
10             62     E
11            129     C
12             52     G
13             27     A
14            102     A
15            101     C

I'm trying to write a query to get the TOP 5 CATEGORY_ID's, first ordered by overall COUNT, but then based on that group use the other CATEGORY_ID's in that group regardless of their COUNT. So, if I wanted to TOP 5 of the above based on this rule (which I probably explained somewhat poorly), my result would be:

CATEGORY_ID   COUNT   GROUPING
6             25      F <-- THE LOWEST COUNT OVERALL
8             59      F <-- THE NEXT LOWEST IN GROUP 'F'
13            27      A <-- THE NEXT LOWEST OVERALL
7             64      A <-- THE NEXT LOWEST IN GROUP 'A'
14            102     A <-- THE NEXT LOWEST IN GROUP 'A'

I've looked a lot here and elsewhere (tried things like RANK(), DENSE_RANK(), GROUPING SETS, and more - mostly as stabs in the dark) and have hit walls all around.

EDIT: One additional thing is that I need to break ties of COUNT randomly. So, for example, if COUNT is 0 for all rows, then the first group returned should be random. I have tried this by adding NEWID() to the ORDER BY in both answers below, but with no luck.

Thank you.

Answer 1

; with groups as (
  select
    grouping,
    min(count) as group_min
  from categories
  group by grouping
)
select top 5 c.category_id, c.count, c.grouping
from categories c
join groups g on c.grouping = g.grouping
order by g.group_min, c.count

Sql Fiddle

Edit:

To randomize in case of ties, you can add a random order to each group using row_number() and newid():

; with groups as (
  select
    grouping,
    row_number() over (order by newid()) as random,
    min(count) as group_min
  from categories
  group by grouping
)
select top 5
  c.category_id, c.count, c.grouping
from categories c
join groups g on c.grouping = g.grouping
order by g.group_min, g.random, c.count

Sql Fiddle