Looking to upgrade old bike

[Demon4231]

I have an old Firenze GL5000 15 speed which I am looking to upgrade a few parts. This would be my first time doing any kind of upgrades and just want to check to make sure I'm doing everything right before I order some parts. I plan on changing the bottom bracket, crankset, and cassette. I measured the BB but I'm not sure if I did it correctly, the attached images are the measurements I have. Will the parts I've selected below work?

Here are the parts list I have come up with.
Shimano Tapered Spindle Bicycle Bottom Bracket - UN26
BIKEHAND Bike Bicycle Shimano Bottom Bracket Removal Remover Tool
Shimano M361 Hybrid Crankset (Black)
Shimano CS-HG20 7 Speed Cassette

For some reason the images wont show up here so here's the links instead
Frame Measurement
Spindle Measurement

 

[dabac]

Removing the spindle is one thing, getting the fixed cup out is another. Unless you plan on making a habit of these things, consider having a shop install the cartridge BB for you.
Your rear wheel is almost guaranteed a freewheel hub, and won't take a 7-speed cassette.

 

[dabac]

Also, what are you hoping to achieve with this work?
Nothing principally wrong with a cup & cone BB.
Unless pitted, clean, lube, adjust and ride.

 

[Demon4231]

I was hoping to install everything myself to learn how it all works, and its a cheaper way to go. I will have to look for a freewheel hub, currently it is 5 gears in the back. There is a little bit of room between the frame and lowest gear, would it be possible to upgrade to 7 in the back?

The reason I am changing out the BB is I wanted smaller cranks in the front and I thought it would be easier to install a newer sealed spindle. The cranks in the front are all metal which is a little bit heavier as well.

 

[dabac]

A 5-speed rear usually means 120 mm dropout spacing, while 7-speed usually means 126 mm. It can mean an awkward stretch to get the wheel in.
If the BB is OK, save some money and keep the old BB.
Not much advantage to a replacing.
It'll probably be both cheaper and easier than getting the Old fixed cup out.
If you want lower gears, look for a freewheel with a bigger biggest sprocket instead. Again, cheaper than messing with the crankset. And same results.
Is it a nutted or a quick-release axle?
Nutted axles tends to run long, and would probably allow you to add washers/spacers enough for a 7-speed rear. Not so sure about a q/r axle.
Don't worry too much about weight. The weight of any single component doesn't mean much when compared to the weight of bike + rider.

 

[Demon4231]

The main reason I want to replace the BB is because some of the cranks are bent and it has cotter pins in it which I found to be difficult to work with. The BB is mostly okay with some minor wear to it, but I'm also looking for smaller cranks.

I will look for a freewheel with a bigger sprocket. The axle is nutted and if a 5-speed would work I could still do that, I'm looking for something that can do small/medium hills without a whole lot of work.

 

[CAMPYBOB]

For the price of a crankset, a new BB to go with it...who the Hell uses a cottered crank in 2016?...and a freewheel you can buy a decent used bike off Craigslist.

If you really, absolutely need a 165 MM crank you will have to shop carefully, but some of the newer vintage 'small' frame sizes came with 165's.

 

[Demon4231]

I got the bike for free and put new tires on it and had the rims and gears adjusted. I really don't want to get a new bike since this one seems like it can be upgraded for a decent price. Will the parts I've listed above work with the bike? Minus the cassette of course.

 

[CAMPYBOB]

Yes. you can buy a BB and crankset to replace the cottered crankset and BB. Hell, you could probably find just a spindle and re-use your bearings and BB cups / lockring.

If you are handy with a file, you could probably make your own crankset from empty beer cans and save all kinds of money.

The BB you listed is English threaded. Is your bike English threaded?
We don't know if a triple will clear your chainstay nor do we know if your derailleur will throw it. We don't know what the chainline is on your bike. The shortest length listed is 170 MM. That is road standard.

 

[Demon4231]

I could probably re-use the bearing and everything which I may look into, although a sealed BB doesn't seem to cost a whole lot. I'm not very good with a file and would prefer my bike not to be made out of beer cans haha.

The bike is English threaded and it currently is a triple, I assumed there was a standard size for the gears and I would assume the derailleur would work.

 

[Demon4231]

The chain line is about 39 mm

 

[Froze]

For the price of a crankset, a new BB to go with it...who the Hell uses a cottered crank in 2016?...and a freewheel you can buy a decent used bike off Craigslist.

If you really, absolutely need a 165 MM crank you will have to shop carefully, but some of the newer vintage 'small' frame sizes came with 165's.

I agree with Bob too. Regardless if you got the bike for free Bob makes a good point, by the time you price out the parts and the tools to do the surgery you could buy a used bike and be a lot further ahead, then you could sell your bike for $50.

And I have a feeling that a lot on that bike you have now is not standard parts, thus parts may be extremely difficult to find if not impossible.

 

[rajababa]

Removing the spindle is one thing, getting the fixed cup out is another