Choose The Powerball Numbers!

Dyalog APL, 10 bytes

(5?69),?26

Dyadic ? is ⍺ distinct random numbers in [1,⍵], and monadic ? is a single random number.

Try it here.

CJam, 16 bytes

69,mr5<26mr+:)S*

69,   range(69)
mr    shuffle the generated array
5<    first 5 elements
26mr  random number 0..25
+     concat to array
:)    increment each array element
S*    join with spaces

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MATL, 10 bytes

69 5Zr26Yr

Uses current version (9.2.0) of the language/compiler.

Example

With compiler run on Matlab:

>> matl
 > 69 5Zr26Yr
 > 
66
59
64
56
29
12

With compiler run on Octave:

>> matl
 > 69 5Zr26Yr
 >
2 69 41 44 23
22

The first five numbers are separated by space, not by newline. This is due to Octave's underlying randsample function behaving differently from Matlab's (and has been corrected in a new version of the compiler). Anyway, newline and space are both allowed by the challenge.

Edit (April 4, 2016): Try it online!

Explanation

69 5Zr    % randsample(69,5), without replacement by default. Gives a 5x1 column vector
26Yr      % randi(26). Gives single number
          % implicit display

See relevant Matlab functions: randsample and randi.