My general visitor type visa will expire in 18th august 2014 and i will not be able to travel before 10th of July because of me being busy at work, I have been in the UK few months back for 5 days and this time also I intend to stay for 5 days is it okay if I show the officer a permission to travel letter with the times stated from my job and a letter from my university that proves that I don't intend to stay more then that time.
As long as you have a valid visa and you are legally allowed to enter and remain in the country, the immigration official should not create any issues.
Traveling on a visa more than once is common if it is a multiple entry visa, and since yours is a visitor visa, just make sure your intent is correct and the intent you are traveling with is legally allowed within the bounds of the visa.
As far as the validity of the visa is concerned, as long as you can enter the country before it and you don't overstay, you'll be fine.
Yes, you will be allowed to enter. As long as your visa is valid, your passport is valid and your expected departure is before the expiry of your visa and passport, there will be no problems at the immigration. Ditto for multiple entries.
As an example, my mother-in-law received a 6-month visitor visa to the UK back in December last year and travelled here for about a month from late December. She then returned to her home country.
She came again to the UK last week - about 5 weeks before her visa expiration date - and her expected departure date is on the last day of her visa validity. She had no problem entering the UK.