Pick one of the golfers, say Larry, as the chooser of 
his two team-mates. Any choice Larry makes for his two 
team-mates will determine both teams.  That's because
Larry will play with the two golfers he chose as 
team-mates, and the 3 that he didn't choose will make
up the other team.

The number of ways Larry can choose his 2 team-mates 
from the 5 is:

C(5,2), 5C2, , i.e., the number of 
combinations of 5 things 2 at a time.

Different teachers and different text-books use different 
notations for this. Some just say "5 Choose 2". 

On the TI-83 and 84 calculators you type

5 nCr 2  then press ENTER.  (You get the nCr by pressing 
MATH, left arrow, 3).  

But regardless of what notation you use, or whether you use
the calculator, the formula  or   you will get
10 ways.  Here they are, using only the golfers' initials:

 1. Team {L,J,P} and {B,T,F} play.
 2. Team {L,J,B} and {P,T,F} play.
 3. Team {L,J,T} and {B,P,F} play.
 4. Team {L,J,F} and {B,T,P} play.
 5. Team {L,P,B} and {J,T,F} play.
 6. Team {L,P,T} and {J,B,F} play.
 7. Team {L,P,F} and {J,B,T} play.
 8. Team {L,B,T} and {J,P,F} play.
 9. Team {L,B,F} and {J,P,T} play.
10. Team {L,T,F} and {J,B,P} play.

Edwin