Read log file between two dates

I have to read log file between and my question is how to get only the text in the file wich is between two dates using unix commands?
Every line contain date and I want to get the text in the file which dates are equal or bigger that the FROM date and lower or equal than the TO date.
The format of the date is 13/05/23 01:58.
The second date is for an example 13/05/13 07:50.
Example

Regular expression problem(s) in Bash: [^negate] doesn’t seem to work

When I execute ls /directory | grep '[^term]' in Bash I get a regular listing, as if the grep command is ignored somehow. I tried the same thing with egrep, I tried to use it with double and single quotes, but to no better results. When I try ls /directory | grep '^[term] I get all entries beginning with term – as expected.