No don't accept it - you can get quicker - I started again at 51 ( 31/12/2010) and my first 5 mile race was in March 2011 and was run in 50:41 - I improved that to 41:22 in October - am looking to increase that this October - around 37:30 in October - with an ultimate goal of sub 30 Ocotber 2013 -
Now you say you do one 800 metres and you are shot - that suggests to me that you are trying to run it to quickly - The goal of an interval session like that is to run each session quickly enough that you can fisnish the session but not to quick that you can't finish it - all you have to do is run slightly quicker than your normal race pace - Also as I try and do a couple of tempo runs each week, I tend to do a shorter interval session eg 10 times 90 seconds off a minute recovery or 15 times a minute again off a minute recovery.
My week looks like this
Monday - 3 miles brisk
Tuesday - 5 miles tempo
Wednesday - Interval session as described above
Thursday - 5 miles tempo
Friday rest day - so no more than 2 miles very easy
Saturday 7 miles - run as I feel
Sunday 3 or 4 miles easy.
Now I am not sugesting you copy the above as my rest day tends to be a short run!!! and everyday is not suitable for every one ( I will admit to have run in my 20s and 30s to an OK standard) but after 12 years out of the sport - did really start again using the run walk schedules on here.
So my answer (eventually) to your question is yes you can run faster - but just look at the speed you are trying to run your intervals.
Good luck