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The number of binary trees that can be formed with 5 nodes is given by the Catalan number ( C_n ), where ( n ) is the number of nodes. The formula for the ( n )-th Catalan number is:
[
C_n = frac{1}{n+1} binom{2n}{n}
]
For ( n = 5 ):
[
C_5 = frac{1}{5+1} binom{10}{5} = frac{1}{6} cdot 252 = 42
]
Thus, the number of binary trees that can be formed with 5 nodes is 42.