By clue 4, the letter P is the 3rd letter in the sequence in row 2.
By clue 7, the letter P is the 2nd letter in the order in column 2.
The P in column 2 cannot be in row 2, since that P is in either column 3 or column 4.
So, the P in column 2 is in row 3, with the L in column 2, then in row 4 (clue 2). (1) (2) (3) (4) (5)
++++++
(1)      
++++++
(2)      
++++++
(3)   P    
++++++
(4)   L    
++++++
(5)      
++++++
By clue 1, the H in row 1 must be in column 1 or column 2.
By clue 9, the word HELP is in order in one column, possibly with the space intervening. If this sequence doesn't occur in column 1, but does in 3, 4, or 5, the sequence would have to begin in row 2  but the L would then conflict with the L in column 2. So, the column in which HELP is in order is column 1, with the H in row 1. Since the L in the sequence can't conflict with the L in column 2, row 4, the L in column 1 is in row 3, and the E is then in row 2 : (1) (2) (3) (4) (5)
++++++
(1)  H     
++++++
(2)  E     
++++++
(3)  L  P    
++++++
(4)   L    
++++++
(5)      
++++++ Similarly, if the word HELP occurs in order, with or without the space in it (clue 9), in row 5, the letter in row 5, column 4 would be L  a conflict with clue 3, which says that the last letter in column 4 is the E. So, the word HELP is in order in row 1.
By clue 5, the 4th letter in row 3 is an H.
In row 3, then, the E can't be in column 5; nor, since the E in column 4 is the 4th letter (clue 3), can the E in row 3 be in column 4. The E in row 3 is in column 3. Then in row 1, the E must be in column 2. (1) (2) (3) (4) (5)
++++++
(1)  H  E    
++++++
(2)  E     
++++++
(3)  L  P  E   
++++++
(4)   L    
++++++
(5)      
++++++
Since the L in column 2 is the 3rd letter in that column (clue 2), the H must be in row 5 of column 2, with the space then in row 2. (1) (2) (3) (4) (5)
++++++
(1)  H  E    
++++++
(2)  E     
++++++
(3)  L  P  E   
++++++
(4)   L    
++++++
(5)   H    
++++++
By clue 4, the P in row 2 is in column 4. In row 1, the P in HELP is in column 5. (1) (2) (3) (4) (5)
++++++
(1)  H  E    P 
++++++
(2)  E    P  
++++++
(3)  L  P  E   
++++++
(4)   L    
++++++
(5)   H    
++++++
The L in row 1 is then in column 3 or 4. If the L in row 1 were in column 3 and the space in column 4, in row 2, the H would be in column 3 and the L in column 5. The E in column 4 would be in row 5 (clue 3). The H in row 3 would have to be in column 4 (clue 5), since there couldn't be another space in that column. But then the letter in row 4 of column 4 would be an L, conflicting with the L in row 4, column 2. So, the L in row 1 is in column 4 and the space in column 3. (1) (2) (3) (4) (5)
++++++
(1)  H  E   L  P 
++++++
(2)  E    P  
++++++
(3)  L  P  E   
++++++
(4)   L    
++++++
(5)   H    
++++++
In row 2, the L is in column 3 or column 5. If the L were in column 3 and the H in column 5, the H in row 3 would be in column 4 (clue 5) and the space in column 5. The H in column 3 would be in row 4 and the P in row 5. In column 1, the P would be in row 4 and the space in row 5. The L in column 5 would be in row 5, with the E then in row 4. But the space in column 4 would then be in row 4  no, by clue 6. So, the L in row 2 is in column 5 and the H in column 3. Then the L in column 3 is in row 5, with the P in column 3 in row 4. The P in column 1 is in row 5, with the space in row 4. (1) (2) (3) (4) (5)
++++++
(1)  H  E   L  P 
++++++
(2)  E   H  P  L 
++++++
(3)  L  P  E   
++++++
(4)   L  P   
++++++
(5)  P  H  L   
++++++
By clue 8, the E in row 4 is in column 4 and the H in 5. Then the H in row 3 is in column 4 and the space in column 5, and the space in row 5 is in column 4 and the E in column 5. (1) (2) (3) (4) (5)
++++++
(1)  H  E   L  P 
++++++
(2)  E   H  P  L 
++++++
(3)  L  P  E  H  
++++++
(4)   L  P  E  H 
++++++
(5)  P  H  L   E 
++++++
