Suppose the coins have to be in the same "slots" as they started:

If there are only three open slots to the left of the coins  there is exactly one 5-move solution (Tristan’s Solution) and exactly one 4-move solution:

_ _ _ X X X X O O O O
X O O X X X _ _ _ O O
X O _ _ _ X O X X O O
X O X X O X O _ _ _ O
X O X _ _ _ O X O X O
 _ _ _ X O X O X O X O

_ _ _ X X X X O O O O
X O O X X X _ _ _ O O
X O _ _ _ X O X X O O
X O X X O X O _ _ _ O
_ _ _ X O X O X O X O

If there are only three open slots to the left of the coins  there is exactly one 5-move solution and exactly one 4-move solution:

X X X X O O O O _ _ _
X X _ _ _ O O O X X O
X X O O X O _ _ _ X O
X _ _ _ X O X O O X O
X O X O X _ _ _ O X O
X O X O X O X O _ _ _

X X X X O O O O _ _ _
X X _ _ _ O O O X X O
X X O O X O _ _ _ X O
X _ _ _ X O X O O X O
X O X O X O X O _ _ _

If there three open slots both to the left and the right of the coins  two new 5-move solutions are gained  with no new 4-move solutions:

_ _ _ X X X X O O O O _ _ _
_ _ _ X X _ _ _ O O O X X O
_ _ _ X X O O X O _ _ _ X O
_ _ _ X _ _ _ X O X O O X O
O X O X _ _ _ X O X O _ _ _
_ _ _ X O X O X O X O _ _ _

_ _ _ X X X X O O O O _ _ _
X O O X X X _ _ _ O O _ _ _
X O _ _ _ X O X X O O _ _ _
X O X X O X O _ _ _ O _ _ _
_ _ _ X O X O _ _ _ O X O X
_ _ _ X O X O X O X O _ _ _

Notice that the two new solutions are slack cheats off the two old 4-move solutions. The 4-move solutions can also be spring boarded into cheap 6-move solutions.