That might be pushing it a little too close. I ran a 55W card successfully on a Dell Inspiron Small Desktop 3647 with a 220W power supply (216 available on the 12V rail).
The 1050Ti is a 75W card. So, 20W more. However, your i5 is a 65W TDP cpu. My system was running a Haswell Pentium, which was 53W.
So, net, you're adding 37W to what I was doing, with only 20W more on the PSU than I had.
Assuming a small motherboard, not a lot of fans, a single hard drive.... I want to say that it SHOULD work, but it's cutting it close. Also, it's likely you'd need a 1050Ti that does NOT use an external power connector, as I would almost guarantee that your existing PSU doesn't have a PCIe power connector for video cards.
Also, check the...