Answer– 94153

Explanation-
Let the number be VWXYZ

Conditions:

(1) V + X = 10
(2) V = Z^2 => V = 4 / 9 and Z = 2 / 3  (V = 1 => Z = 1 which is NOT allowed.) 
(3) Y = W + 1
(4) V + W + X + Y + Z = 22

Applying (1) and (3) in (4) => 10 + 2W + 1 + Z = 22

=> 2W + Z = 11   (5)

Exploring possible values from (2):

(a) If V = 4, Z = 2 then (5) =>  2W = 9 which is Impossible.
(b) If V = 9, Z = 3 then X = 1, W = 4, Y = 5.

Hence the code is 94153.

ponder on this password too:
1 5 9 6 1

1st no.= 1*1=1
3rd no.=10-1=9
4th no. = 2nd no. +1 => 5+1=6
total of digits => 1+5 +9 +6 +1= 22  kaboom!!!

Answer:94153
We know that the answer will have the following pattern.
x       y       10-x      y+1       sq.root(x)
We know that x cannot be taken as 5 as 5^2=25>22.
If we take x as 4^2=16,
1st digit=16
5th digit=4
16+4=20
only 2 is left and thus it is not possible.
Only if  x is taken as 3 will we get a correct answer .