The thermal X-ray emission from core-collapse supernovae (SNe) is of great interest as a probe of both the nature of the progenitor star and the evolution of the shock waves originating from the explosion. The forward shock resulting from the SN explosion expands into the circumstellar medium created by mass-loss from the progenitor star. The X-ray emission arising from the shock heated material depends on the density of the medium it is expanding into, and thus can be used to understand the density structure of the medium. The SN shock waves travel much faster than the winds from the progenitor star, and therefore can trace several decades to centuries of wind density evolution in the span of a few years. In order to understand the evolution of SNe into supernova remnants (SNRs) it is desirable to construct the X-ray light curves of supernovae over long periods of time, out to late epochs. We have analyzed archival Chandra observations of five of the oldest known X-ray supernovae — SN1970G, SN1968D, SN1959D, SN1957D and SN1941C — and successfully constructed the light curves of three of them (SN1970G, SN1968D and SN1957D) over several decades. The X-ray luminosity of these supernovae is found to decline steeply as t-2.5 (though with large errorbars), likely suggesting expansion into a non-steady wind. No increase in the X-ray emission from SN 1970G is found at later epochs contrary to what has been previously published in the literature. In general all five SNe show X-ray luminosities that are of comparable magnitude, even though their electron temperatures may vary by factors of a few. We compared the late-time X-ray luminosities of these SNe to those of older SNRs in the Galaxy and the LMC, and found that many older SNRs have higher X-ray luminosity. These X-ray bright SNRs may arise from higher luminosity SNe, but can also be explained by the fact that the X-ray luminosity should increase as the remnant expands during the Sedov phase. Our results demonstrate the necessity for multi-wavelength follow-up of old (~several decades) supernovae in multiple wavelengths, in order to better understand fundamental ideas of SN and shock evolution.