Sampling vs repetition code
You are mixing up notions of matched filtering (e.g. using an LTI system) with a correlation receiver implementation of the same.  The correlation receiver is an "integrate and dump" device -- a time-varying circuit -- whose output resets to zero (that's the dumping part) immediately after the output is sampled at the correct time (once each symbol interval) so that the correlator starts with initial condition $0$ for each symbol correlation. Note that the correlation receiver output does not equal the matched filter output except at the sampling instants.  A simple illustration of this point is available towards the end of my answer to 
Understanding the Matched Filter

So, if you sample the correlation receiver output multiple times (five times in your case) during one symbol interval, the question arises as to what happens to the correlator after each sampling?  Is it dumped after each sample, or does it continue to accumulate the correlation until the final sample is taken and the correlator is dumped right afterwards?  In the former case, the samples are independent random variables while in the latter case, they are dependent.  Also, how do you propose to process these samples?  In the former case, the optimum thing to do would be to add up the five samples (which has the same result as running the correlator over the entire symbol interval and sampling just once at the end of the interval) while in the latter case, the optimum thing to do would be be discard the first four samples and just keep the last one.  Here, optimum is with respect to the signals being received in white Gaussian noise; if your noise is something else, then you need to specify what it is, and to what extent is the concept of matched filtering or correlation even justified as the right thing to do.