To solve this, we'll simplify each term one at a time:

First, we'll find the value of 2.35 - 2 4/7:

2 4/7 is equal to 2 + 4/7 = 2 28/7 = 30/7

So, 2.35 - 30/7 = 2.35 - 4.28 = -1.93

Next, we'll substitute this value back into the original expression:

5 3/7 - (-1.93) + 5.45

Now, we'll calculate the first term:

5 3/7 = 5 + 3/7 = 5 21/7 = 26/7

So, the expression becomes:

26/7 + 1.93 + 5.45

Now we'll add up the fractions:

26/7 + 1.93 + 5.45 = (26 + 1.93 + 5.45)/7 = 33.38/7 = 4.769

Therefore, 5 3/7 - (2.35 - 2 4/7) + 5.45 = 4.769.