General :: SED Or AWK - Remove Every 4 Of 5 New Lines

I have a file that looks like this:

1
2 3 4 5 6 7 8 9
10 11 12 13 14 15
16 17 18 19 20 21
22 23 24
1
2 3 4 5 6 7 8 9
10 11 12 13 14 15
16 17 18 19 20 21
22 23 24
1
2 3 4 5 6 7 8 9
10 11 12 13 14 15
16 17 18 19 20 21
22 23 24
...
I would like to reformat it to look like this:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
...
Is there a nifty awk/sed one-liner to do this operation?