First of all, congrats on putting together what sounds like a pretty decent work wardrobe. I'll say "buy more" a few times in this post as a suggestion, but it's not as if you aren't in good shape most likely. At some level only you can know what is right for you when it comes to clothes, but I'd say this looks pretty decent. I work in a business casual environment myself and do not have to wear a suit that often. Not sure on exact ratios, but I definitely think owning more sport coats than suits is a good idea. Trousers should always outnumber odd jackets since you need to get trousers pressed more frequently than odd jackets. Shirts should outnumber trousers. I have around a 1:1 tie to shirt ratio and I think that is ideal as it gives you access to a large number of looks and prevents you from always wearing one or two ties with a particular shirt. Sweaters is really a personal thing and depends on how much you like the sweater over dress shirt look or how much you wear a sweater casually. My ideal ratio (business casual or suit not required for work) is probably something like this:
1:2:3:6:6 (i.e. for every suit, two sport coats, three pairs of odd trousers, six dress shirts and six ties). Note that this excludes casual pants, polos, etc.
I actually think the number of shoes you need is defined more by your environment and taste than a ratio to anything else in your wardrobe. If you wore a suit everyday, you'd only need to be able to rotate enough suit appropriate shoes and could make do with three pairs (rotate three, then rotate two when you have to send the third to the cobbler). In a more casual environment, you need three pairs of shoes that you can rotate that work without a tie, plus something you can wear with a more formal outfit when the occasion calls for it. Add in any desire for variety (color, design, etc.) in shoes and your needs increase.
Suits - If you wear one rarely, then two suits is going to be sufficient. It's not worth bothering with different fabric weights for different weather if you don't wear a suit that often anyways. Not sure what you have but the first two suits will ideally be navy solid and grey solid.
Sport Coats - Four is a decent collection. If you wear these a lot more than suits, however, and like to wear a jacket during the summer, it might be worth your while to expand this number slightly. The key here is making sure your sport coats are versatile. If they're overly loud or noticeable, you need more.
Pants - Eight is a good number provided you wear them all regularly. If you have a few favorites that you wear all the time, I'd suggest getting a few more pairs of them. In general, if you can wear a pair of pants once a week and let it rest in your closet for a week, that's pretty good.
Shirts - Fifteen is a good number of shirts to own. You could buy more shirts, but it's not necessary.
Ties - Get more. The number you have is fine if you liked and wore them all regularly, but it sounds like some just hang on the rack. We inevitably go through our entire shirt wardrobe even if we have some favorites but tend to gravitate more towards specific ties. Having more ties that you wear regularly lets you put together many more looks.
Shoes - Five is fine. I don't really think that there's an ideal ratio for shoes compared to the rest of your wardrobe. You just need enough so that you never have to wear a pair two days in a row and that you have different styles for different levels of formality (e.g. AE Park Avenue or the like for suit and tie, perhaps a brogued blucher or monkstrap for less formal occasions and loafers if you like them).
If you're looking to expand, I'd buy more shoes, a sport coat, ties and shirts. Linen pants are nice too. If you'd like recommendations, perhaps post some more details on what you own.