If you switch out your cassette, you might want to also switch out the chain as well, depending on how much wear it has.
Are you sure your big chainring is a 56 tooth? I have never heard of a chainring that big.
I don't doubt you are having trouble climbing hills with your current set up. Your lowest gear of 39 - 23 is a fairly big 44.7 gear inches.
Switching to a 28, will help a little, as you will get to 37 gear inches but will it be enough? That IDK. I can only speak for myself in saying it wouldn't be low enough for me. For the riding I do and my level of fitness, I look for a low gear of 25 or 26 gear inches. On a 39 tooth small chainring paired with a 34 tooth cog gives you 30 gear inches, and 36 tooth, 28 gear inches. The problem of course is, you will have fairly huge jumps between gears, and it might not even work with your back derailleur.
You might want to switch to a Compact double set of chainrings 50/34. AND switch out your cassette to one with 32 tooth biggest cog. Then you are down to a very usable 28 gear inches.