To solve the problem, we follow these steps:

Step 1: Find the first term (a_1)

Given (S_n = 2a_n - 1), when (n=1):
(S_1 = a_1 = 2a_1 - 1)
Solving for (a_1):
(a_1 = 1)

Step 2: Derive the sequence type

For (n \geq 2), (a_n = Sn - S{n-1}):
(a_n = (2an -1) - (2a{n-1} -1))
Simplify:
(a_n = 2an - 2a{n-1})
(an = 2a{n-1})

This is a geometric sequence with common ratio (r=2) and first term (a_1=1).

Step 3: Calculate (a_5)

The (n)-th term of a geometric sequence is (a_n = a_1 \cdot r^{n-1}):
(a_5 = 1 \cdot 2^{5-1} = 2^4 = 16)

Answer: (\boxed{16})

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