Answer:
Y=8 and X=21
Step-by-step explanation:
The key to solving word (story) problems is to learn how to translate words and phrases into concise, precise math expressions (variables and operations).  Make a table and add to it as you do problems:
       is              means           =
     more than                        +
       twice                              2*x
       sum                               +
       of                            usually means multiply
      ...
 
Assign variables.  Try to assign variables to the values the problem asks you to find.
In this problem, there are two variables.   Let x = one number;   y = other numbers
 
Translate:
  "One number is 5 more than twice the other number"    means
             x          =    5    +        2     *      y
  "sum of the two numbers is 29"     means
       x   +   y                    = 29
 
Now, the easy math.
 
Use the value for x from the first equation and substitute that into the second equation:
     (5 + 2y)      +     y       =  29
      5 + 3y = 29                    (collect terms)
            3y = 24                (subtract 5 from both sides)
              y = 8
 
Now, put that value of y into either equation to solve for x  (Which equation is easier??)
      x + 8 = 29
        x  = 21                 (subtract 8 from both sides)
 
Checking (very important):
  Is 21 really 5 more than 2(8)?
       21 = 5+16     ?
       21  =  21? yes
  Is  21 + 8 = 29  ?
         29 = 29? yes
 
p.s., learn the process, don't just get the right answer;  there will be lots of problems that are solved the same way!