Maximum depth or height of the below tree is 3.

Example Tree
Example Tree

Recursively calculate height of left and right subtrees of a node and assign height to the node as max of the heights of two children plus 1. See below pseudo code and program for details.
Algorithm:
 maxDepth()
1. If tree is empty then return 0
2. Else
     (a) Get the max depth of left subtree recursively  i.e., 
          call maxDepth( tree->left-subtree)
     (a) Get the max depth of right subtree recursively  i.e., 
          call maxDepth( tree->right-subtree)
     (c) Get the max of max depths of left and right 
          subtrees and add 1 to it for the current node.
         max_depth = max(max dept of left subtree,  
                             max depth of right subtree) 
                             + 1
     (d) Return max_depth
See the below diagram for more clarity about execution of the recursive function maxDepth() for above example tree.
            maxDepth('1') = max(maxDepth('2'), maxDepth('3')) + 1
                               = 2 + 1
                                  /    \
                                /         \
                              /             \
                            /                 \
                          /                     \
               maxDepth('1')                  maxDepth('3') = 1
= max(maxDepth('4'), maxDepth('5')) + 1
= 1 + 1   = 2         
                   /    \
                 /        \
               /            \
             /                \
           /                    \
 maxDepth('4') = 1     maxDepth('5') = 1
Implementation:
#include
#include
 
 
/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node
{
    int data;
    struct node* left;
    struct node* right;
};
 
/* Compute the "maxDepth" of a tree -- the number of
    nodes along the longest path from the root node
    down to the farthest leaf node.*/
int maxDepth(struct node* node)
{
   if (node==NULL)
       return 0;
   else
   {
       /* compute the depth of each subtree */
       int lDepth = maxDepth(node->left);
       int rDepth = maxDepth(node->right);
 
       /* use the larger one */
       if (lDepth > rDepth)
           return(lDepth+1);
       else return(rDepth+1);
   }
}
 
/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node = (struct node*)
                                malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
   
    return(node);
}
   
int main()
{
    struct node *root = newNode(1);
 
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
   
    printf("Hight of tree is %d", maxDepth(root));
   
    getchar();
    return 0;
}

Time Complexity: O(n) (Please see our post Tree Traversal for details)