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2015-12-22T19:12:05+05:30

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1 1 1 1 = 5

Divide 5 by 1 =  \frac{5}{1} 5

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2 2 2 2 = 24

Divide 24 by 2 =  \frac{24}{2} 12
Take the previous number, which is 5.
Notice that, (5 × 2) + 2                how did 2 come ?  [ (2 × 1) + 0 = 2 ]
                    10 + 2 = 12

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3 3 3 3 = 93

Divide 93 by 3 =  \frac{93}{3} 31
Take the previous number, which is 12.
Notice that, (12 × 2) + 7          how did 7 come ?  [ (3 × 2) + 1 = 7 ]
                    24 + 7 = 31

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4 4 4 4 = 272
                                 
Divide 272 by 4 \frac{272}{4} 68
Take the previous number, which is 31.
Notice that, (31 × 2) + 6          how did 6 come ?     [  (4 × 1) + 2 = 6  ]
                    62 + 6 = 68

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To find out the value of 5 5 5 5 -

1. we have to take the previous number (quotient in the last division)
2. multiply it with 2
3. a. find out the product of the frequent no. in the serial (in here, it is 5) and either 1 or 2   b. add sequential no. to the product
(how to determine 1  or 2 and the sequential no. ?
they keep switching all the time.
see in 2 2 2 2 the frequent no. in the serial was multiplied by 1
then, in 3 3 3 3, it was multiplied by 2
and, in 4 4 4 4, it was multiplied by 1

so, 1 -> 2 > 1 -> 2, like this.
in 5 5 5 5, it will be multiplied by 2, as in 4 4 4 4 it was multiplied by 1

SEQUENTIAL NUMBER:
see in 2 2 2 2, the sequential number is 0
then, in 3 3 3 3, it was 1
and, in 4 4 4 4, it's 2

so, in 5 5 5 5, it will be 3
)
c. add the whole thing with the product found in step 2
4. multiply the resulting number with 5 
5. the resulting number is the value of 5555

let's do it, then - 

Step:1:  the previous number was 68
Step:2:  twice the number is 68*2=136
Step:3:  a. the product of 5 and 2 is 10
b. 10 will be added with 3 10+3 13
c. 13 added with 136 - 149

Step:4: The product of 149 and 5 is 745
Step:5: So, the value of 5 5 5 5 is 745

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The values are :

1 1 1 1 = 5
2 2 2 2 = 24
3 3 3 3 = 93
4 4 4 4 = 272
5 5 5 5 = 745

1 5 1
Comment has been deleted
How did you copy my answer and post it ???
Why did you copy my answer and post it ???
My answer is too complicated, thatswhy I gave the simpler logic.
I am the one who gave the another logic.