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The convolution of hyperspectral data to Landsat 5 TM bands is done by using the spectral response function (SRF, or Relative Spectral Response [RSR]) of Landsat 5 TM sensor. The ranges of each valid band are determined by the full width at half maximum bandwidth (FWHM) of each SRF. The central wavelength is also determined from this range. However, when doing the spectral convolution, should I consider just the SRF whithin the valid band range (red line) of Landsat 5 TM sensor, or the whole SRF which also lies out of the valid band range (the response of red and black lines)? I have convolved using both alternatives, but I'm not sure which one is the right.

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You should use only the red line, the FWHM, as is recomended in USGS Spectral viewer(Here):

To simulate how a sensor detects a surface feature in a given spectral band, the feature's spectrum is "convolved" with the sensor's RSR. This is based on the average of the wavelength extents of the full width at half maximum values.

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