Biggest problem I could think of, is the PSU - typically,. the includes PSUs are capable for stock operations (ie what it shipped with from the factory) and not a bunch more.
180W unit shipped with that system, powering an R5 330 - and 18W part.
You're talking about replacing with a 75W TDP card.
With an i5-6400 + 1050TI, you've got a max power draw in the ~150W range.
Might be doable on that PSU, might not..... I really can't find much on it.
I think this might be (or be very similar to) the motherboard in question? If so, it uses a standard 24pin ATX and 4pin EPS connector(s), so the PSU could be replaced (although you may have to transplant into another case to fit an ATX PSU if it's a non-standard size).