How do you grep a file and get the next 5 lines

Here is a sed solution:

sed '/19:55/{
N
N
N
N
N
s/\n/ /g
}' file.txt

Some awk version.

awk '/19:55/{c=5} c-->0'
awk '/19:55/{c=5} c && c--'

When pattern found, set c=5
If c is true, print and decrease number of c

You want:

grep -A 5 '19:55' file

From man grep:

Context Line Control

-A NUM, --after-context=NUM

Print NUM lines of trailing context after matching lines.  
Places a line containing a gup separator (described under --group-separator) 
between contiguous groups of matches.  With the -o or --only-matching
option, this has no effect and a warning is given.

-B NUM, --before-context=NUM

Print NUM lines of leading context before matching lines.  
Places a line containing a group separator (described under --group-separator) 
between contiguous groups of matches.  With the -o or --only-matching
option, this has no effect and a warning is given.

-C NUM, -NUM, --context=NUM

Print NUM lines of output context.  Places a line containing a group separator
(described under --group-separator) between contiguous groups of matches.  
With the -o or --only-matching option,  this  has  no effect and a warning
is given.

--group-separator=SEP

Use SEP as a group separator. By default SEP is double hyphen (--).

--no-group-separator

Use empty string as a group separator.