Maybe a GT 1030 would work. It's a 30W card.
I had an Inspiron 3647 with what I think was the same 220W PSU . . with 18A (thus 216W) available on the 9V rail. I used an R7 250E (55W, which is different from the R7 250 non-E which draws up to 65W), although the Sapphire version I used called itself the R7 250 Low Profile (it was a 250E rather than a 250, though).
I think it's basically the same as the HD 7750. It'll improve things a little bit, and my son used it without issue. BUT... he had a Haswell era Pentium CPU. The i5 consumes more power, and consequently would push you over the edge, I think. But, I think your 7570 uses 60W, and I'm surprised that's working without giving you trouble with the PSU.
Which exact i5 are you using?