Okay, let's go from the top.
- Always use 
implicit none. If you don't use implicit none, you will get bugs. 
- Your indenting looks a bit like fixed-form fortran, but you're actually using free-form fortran (and we are in 2022, everyone should be using free-form fortran), so your indentation should really be consistent.
 
- You don't have an 
end program line or an enddo line, presumably because this is just a snippet of code. 
- As VladimirF points out, the line 
do i=1,11 must be one line, not two. 
Lets fix these first, to give
program pressure
  implicit none
  
  real pk(11), zp(11), g, rz,z,dz, p_atm
  
  g= 9.81
  z(i)=(0:5:-50)
  dz= -5
  p_atm= (/0.97, 1.02, 1.04, 1.03, 1.01/)
  
  do i= 1,11
    d= z(i)
    
    if(d.GT.-10.0) then
      rz= 1020.0
    elseif(d.LT.-10.0 .and. d.GT.-50.0) then 
      rz= 1020.0+(0.25*(ABS(d+10.0)))
     
    if d == 0
      p(i)= -(((-rz*g)*dz))+p_atm)
    else
      p(i)= -(((-rz*g)*dz))+p(i-1)
    endif
    open(20,file='pressure.txt', status='unknown')
    rewind(20)
    write(20,25) 'Model Day', '1', '2', '3', '4', '5'
    write(20,26) 'Patm (10^5 Pa)', '0.97', '1.02', '1.04', '1.03', '1.01'
    26   format(a14,12F9.2)
    25   format(a10,12F9.0)
  enddo
end program
Okay, now we can try compiling and see what happens. The compiler is going to shout at us for a number of reasons:
- The variables 
i, d and p have not been declared. 
z(i) either means a function call or an array element access (from context, you want the latter), but z is defined as a scalar variable, not a function or an array. 
p_atm is being initialised as an array, but was declared as a scalar. You're also trying to add p_atm as a scalar, so let's add a loop over these pressures. 
- The 
if and endif statements don't match; you need to endif your first if block. 
- Your format strings don't match: you're printing character strings, but formatting them as floats (
'0.97' is a character string, 0.97 is a float). 
- Your second 
if statement needs to have appropriate brackets and a then. 
- You close more brackets than you open in your first 
p(i)=... line. I'm going to have to guess here. 
- The comparison 
d==0 is a really bad idea. Never compare floats for equality. Let's replace this with i==1. 
Okay, let's fix these problems:
program pressure
  implicit none
  
  real pk(11), zp(11), g, rz, z(11), dz, p_atm(5), p(11), d
  integer i,j
  
  g= 9.81
  z(i)=(0:5:-50)
  dz= -5
  p_atm= (/0.97, 1.02, 1.04, 1.03, 1.01/)
  
  do j=1,5
    do i= 1,11
      d= z(i)
      
      if(d.GT.-10.0) then
        rz= 1020.0
      elseif(d.LT.-10.0 .and. d.GT.-50.0) then 
        rz= 1020.0+(0.25*(ABS(d+10.0)))
      endif
     
      if (i == 1) then
        p(i)= -(((-rz*g)*dz))+p_atm(j)
      else
        p(i)= -(((-rz*g)*dz))+p(i-1)
      endif
      
      open(20,file='pressure.txt', status='unknown')
      rewind(20)
      write(20,'(a14,5a9)') 'Model Day', '1', '2', '3', '4', '5'
      write(20,'(a14,5a9)') 'Patm (10^5 Pa)', '0.97', '1.02', '1.04', '1.03', '1.01'
    enddo
  enddo
end program
Okay, now we get to initialising z. The most straightforward way of doing this is with a simple loop:
do i=1,11
  z(i) = 5-5*i
enddo
but if you want to get fancy with it, you can use an implicit do loop:
z = [(5-5*i, i=1, 11)]
Also, given your output file header, it probably makes sense to store p for all values of i and j, so let's make it a 2D array. Let's also move the file-writing to after we've calculated all values of p. Then, making a few modernisations along the way, your program looks like:
program pressure
  implicit none
  
  real :: pk(11), zp(11), g, rz, z(11), dz, p_atm(5), p(11,5), d
  integer :: i,j
  
  g = 9.81
  z = [(5-5*i, i=1, 11)]
  dz = -5
  p_atm = [0.97, 1.02, 1.04, 1.03, 1.01]
  
  do j=1,5
    do i=1,11
      d = z(i)
      
      if (d > -10.0) then
        rz = 1020.0
      elseif (d < -10.0 .and. d > -50.0) then 
        rz = 1020.0 + 0.25*abs(d+10.0)
      endif
     
      if (i == 1) then
        p(i,j) = -(-rz*g*dz)+p_atm(j)
      else
        p(i,j) = -(-rz*g*dz)+p(i-1,j)
      endif
    enddo
  enddo
  
  open(20, file='pressure.txt', status='unknown')
  write(20,'(a14,5a9)') 'Model Day', '1', '2', '3', '4', '5'
  write(20,'(a14,5a9)') 'Patm (10^5 Pa)', '0.97', '1.02', '1.04', '1.03', '1.01'
  do i=1,11
    write(20,'(5f9.2)') p(i,:)
  enddo
  close(20)
end program