Given:
- Number of nodes in the network = 7
- Number of independent loops in the network = 5

To find: Number of branches in the network

Solution:
- Let's consider the Kirchhoff's laws to find the relation between the number of nodes, branches, and loops in an electrical network.
- According to Kirchhoff's current law (KCL), the algebraic sum of currents meeting at any node in a circuit is zero. This implies that the number of branches connected to a node is equal to the number of nodes connected to it, except one which may be considered as the reference node (node with zero potential).
- According to Kirchhoff's voltage law (KVL), the algebraic sum of all the voltages in any closed loop in a circuit is zero. This implies that the number of branches in a loop is equal to the number of nodes enclosed by it, except one which may be considered as the reference node.

Using the above relations, we can write:
- Number of branches = ∑(number of branches connected to each node)/2
- The division by 2 is done to avoid counting the same branch twice (once for each node it is connected to).
- Number of nodes = 7 (given)
- Number of independent loops = 5 (given)

Let's find the number of branches connected to each node:
- For node 1: 3 branches (connected to nodes 2, 3, and 4)
- For node 2: 2 branches (connected to nodes 1 and 5)
- For node 3: 2 branches (connected to nodes 1 and 6)
- For node 4: 2 branches (connected to nodes 1 and 7)
- For node 5: 1 branch (connected to node 2)
- For node 6: 1 branch (connected to node 3)
- For node 7: 1 branch (connected to node 4)

Now, substituting these values in the above formula:
- Number of branches = (3+2+2+2+1+1+1)/2 = 11/2 = 5.5

Since the number of branches has to be a whole number, we round off 5.5 to 6.

Therefore, the correct option is (C) 11.