Question Can I fit a replacement PSU in my Dell PC case ?

Aug 1, 2023
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I have a Dell Vostro 3888. I have been wanting to upgrade It but the PSU inside It Is pretty small.
It isn't a cube like the PSU I am buying, it is a cuboid but a small one. I searched all over for its name but I couldn't find It, all I know is the PSU was made by Dell, here is a pic for reference:
41klOB8ptUL._AC_US40_.jpg

The one In the pic is not the same as the one i have but it is the same shape. Will I be able to get a new PSU ?
I know it won't fit in the case but it could fit if I put it in horizontally.
 
my pc specs are :
i5-10400 (no letter at the end)
2x8gb ram 2666 mhz
350 watt psu (lookin to get a 500 watt if needed)
gt 710 2gb vram
120 gb ssd
512 gb ssd
1tb hdd
 
If the PSU has a 6 pin and 8 pin PCIe it's useable. Cheaper than a new case, motherboard and ATX PSU.
i have noticed that the arc a750 is a bit big and i measured my case and saw the measurments of the arc a750 and it can't fit in my case so i have decided to get a new motherboard, case and psu. Are there any good quality components that you would recomend that are compatible with the i5-10400 ?