https://support.hp.com/us-en/product/hp-pavilion-slimline-s5700-desktop-pc-series/5035352/model/5049556/document/c02623675
It looks like that system should have a PCIe x16 slot available, which is what you would want for installing a graphics card. A 220 watt power supply is pretty low wattage, but the other components shouldn't be particularly power hungry, so you could likely get away with installing an efficient lower-end card like a GT 1030, which only draws around 30 watts, and usually comes in a low-profile (slimline) size. A GT 1030 would even exceed the recommended requirements for that particular game by a fair amount.
Since that game is a bit older, even a previous-generation GT 730 would likely be enough to run it rather well, though a GT 1030 should be more than twice as fast, so it's probably only worth considering a 730 if you can find it for a substantially better price. Currently, at least in the US, you should be able to find a GT 1030 new for somewhere around $100, while GT 730s should start for around $70 new. Again, just make sure you look for a low-profile version. Most of them should be, but there are some wide GT 1030s and 730s as well.
Also, if you go for a GT 1030, note that if you use an older monitor that only has the option to connect with a VGA cable, the 1030 doesn't support VGA anymore, so you would also need an active adapter to convert to VGA from another connection such as HDMI, and such adapters can be found for less than $10 on Amazon. A GT 730 should include a VGA port built in, but again, it is a weaker card.