I think you mean 5 activities/games in the morning and 5 activities in the afternoon - in which case use the following schedule:
Morning
G1 G2 G3 G4 G5
(A B) (C D) (E F) (G H) (I J)
(I E) (H J) (G B) (F C) (D A)
(J F) (G I) (H A) (E D) (B C)
(G D) (F A) (C J) (B I) (E H)
(H C) (E B) (D I) (A J) (G F)
Afternoon
G6 G7 G8 G9 G10
(F H) (J E) (B D) (I A) (C G)
(E G) (I F) (A C) (J B) (H D)
(D J) (A G) (I H) (C E) (F B)
(C I) (B H) (J G) (D F) (A E)
(A B) (C D) (E F) (G H) (I J)
Notice that the last round, repeats the pairings from the first round.