Etydhv

I have an old bike with a cassette and chain that needs replacement. The problem is that I can't identify what kind of cassette it is or how to remove it.

There are 14 teeth on the smallest cog and 28 teeth on the largest cog on the cassette. How do I remove it? There are only two nuts.

Will the bike take any Shimano chain (that matches number of links of the current chain?)

From comment:

I took the wheel off, i watched the video from Parktool but couldn't see any groves inside the cassette

If you are replacing the freewheel anyway. I would personally not buy the tool as you can easily remove a freewheel with a light hammer and a punch or screwdriver if you don't have a punch/drift. Look at the two recessed dots on the face of the freewheel. Place the punch on one of the dots and strike down it in a clockwise direction it should easily come loose without damage and save you buying a tool you may never use again. As long as you don't hit too hard you won't cause any damage to it and if you are replacing the freewheel anyway it seems the best option to me.

If it's 5 speed, it's probably a freewheel rather than a modern style cassette that slides on a freehub.

Park Tools do a tutorial video on how to change one:

Additional information can be found on the Park Tools blog

Regarding the replacement chain and freewheel (as many people have pointed out you have a freewheel not a freehub and cassette):

The interface between hub and freewheel is standardized so any 5 speed freewheel with the appropriate sprocket sizes will work.

Chains are sold with more links than needed then cut down to size and joined, so you don't buy one with the proper number if links. Chains are specific to the number of sprockets on the freewheel/cassette, you will need a 7 speed or less chain (5, 6 and 7 speed chains are the same, the differences start at 8 speed).

Here's a Park tool Video on chain sizing and joining

https://www.parktool.com/blog/repair-help/chain-length-sizing

Having spent some significant time taking bits of bikes apart when I was younger, my experience is the opposite of David's. My experience is that freewheels are very reluctant to move when applying a hammer and drift to the "two dots". Especially if the wheel and freewheel have had years of being married together, they'll seriously resist divorce. And if you hammer in the wrong direction, that plate with two dots is a cover for the ball races and you'll have a floor full of tiny ball bearings.

I'm going to give you a slight frame challenge instead. If this is an old bike, I would not be at all surprised if the wheels were steel, or at best some low-grade alloy. The spokes are probably in a bad way, and you don't really want to be stuck with an old-style freewheel anyway. If you're planning on chucking the freewheel anyway, why not chuck the whole thing and buy a decent new alloy wheel and cassette? No need to remove anything.

Don't forget that you want a new chain as well, whatever you do. Chains wear into the geartrain, so if you change the cogs then you should change the chain too. They're pretty cheap anyway. You'll need a chain remover tool if you haven't already got one, of course.