What do you want to do with the computer? Do you have a video card in mind? What is your budget outside of the pre-built - for the GPU and PSU (as discussed below).
Be mindful that these computers come with pretty weak PSU's, in part because they are not powering GPUs. This means that if you intend to upgrade to a discrete GPU, instead of the integrated, you will also want to upgrade to a good PSU, even if the wattage isn't much higher than the provided one - but the highest these boxes have is 250W, which would be really pushing it, if not fatal, by putting in a discrete GPU.
So, in terms of budget, be mindful that in addition to buying a new video card, you would also want to buy a new PSU.
The 5750 isn't "little old" its just a lower model of the DX11 series, which are the newest models. Anyway, here is a link to the power usage of the 5750: Tom's Thread about 5750 Power usage.
The conclusion is that you want at least a 450 Watt PSU, which is significantly higher than those that come with the computers you linked. You say you have a corsair PSU, what is the wattage on it? (Also if the PSU is older, it is likely to not be as efficient as a new one, which is also true of the newer GPUs - the 5750 should run cooler than your previous GPU).