YES,

Fly reels are for the most part sized for the backing/line wt.
If you want to very the line to rod, keep the line & reel matched.
Putting a heavy line on a lighter wt reel wt will limit your backing.

If you're starting out, I would suggest you stay the line and not mess with it.

When I lived in the Keys, I practiced in my yard. I was lucky to have a 150ft grass area and no trees to target shoot. I used paper plates as targets. Going from 8wt up through 12wt was not easy, as the actions(mostly fast) and lines (mostly sinking) across the wt??  anyway, I would practice a couple of times a week to keep the feel..

All my rods were Sage, reels Sage & Tubor
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Another issue with using a smaller reel is the weight of the reel itself. Having a tip heavy rod will get old fast. Balancing the rod/reel will make casting earlier as will carrying the rod while fishing.

And as the other poster said, putting a 5 weight line on a reel designed for a 3/4 reel will limit backing and maybe even the line itself. In fact, it’s more common to up the reel size a bit in order to balance the rod and also allow for backing content.

I use 65 lb PowerPro for backing as it is the same dia as 20 lb linen backing,, and on my 8 wt reel that's about 150 yds.
Every extra inch of backing is needed for Permit, Bones & Poons

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It's tough to say, but at certain weights the reel is just a line holder.  I've gone a size smaller on a reel before, because of a great deal.  I'm not sure what you are fishing for, but if a trout can run a 100yds of backing, that's going to be a sweet day!  :)  You can always do what I did, I went with Hatch backing, it's stronger and smaller than the normal 20lb backing, so you can probably get more on there if needed.  If not, I would just put on less 20lb backing, 75 yds of backing is still plenty for most scenarios that I would fish a 5wt.

The one catch for me would be how the reel balances.  I think the difference between those two reels is just over a 1/2 oz. , I'm not sure if you'd feel it immediately or not.

Good Luck!

eta -  I think the reel was like $75-100 cheaper, and I still catch fish on it.  I bought the 3/4, and put plenty of backing on it with a 5wt WF line.

now I need to decide if I'm going shooting this afternoon or fishing.

Ross makes very nice reels. You can’t go wrong with a Ross.

Solid choice, Made in America to boot.

Nice fish!  Hopefully, I’ll get a chance to land one.