The annual personal allowance is currently £6,475, so you're correct that an income of £5k would usually mean that you have no Income Tax liability. Note that being a student/in full-time education has no bearing on this.
Note that as a partnership, while you may not have to submit formal accounts to a central body in the way that companies and LLPs do, you will still have to draw up accounts, e.g., to support your tax return. Agreed that there are less formalities involved in a 'straight' partnership than with an LLP.
I assume that you way this because you'll be continuing your existing part-time job? Your employment income will continue to be taxed at source (if appropriate, depending on your level of earnings) under the 'Pay As You Earn' (PAYE) system. However, you'll
also need to register with HMRC as self-employed and complete a self-assessment tax return. Read more about this
hereThere can be tax advantages from structuring a business as a company rather than as a partnership/sole trader, depending on you level of profits. Corporation tax at the small companies rate is 21% on profits of up to £300,000; by contrast, higher-rate Income Tax is 40%. Company profits are also not subject to National Insurance in the way that income from employment or self-employment is.
However, this can leave difficulty in extracting cash from the business (if dividends are taken, Income Tax may be chargeable on company profits that have
already been subject to Corporation Tax), and if the business profits are relatively low (such that your personal income doesn't exceed the higher-rate Income Tax threshold) then the differential between corporate and personal tax rates becomes less favourable. I'd also add that the reasons for structuring a business in a certain way should not be completely governed by tax considerations. As you've already highlighted, there's a not insignificant compliance burden associated with a corporate structure, for example.
There's no need to incorporate a company in order to take on employees, so that's not a relevant consideration here. Sole traders and partnerships can employ people just as a company can.
I would agree that if you're unsure about this it would be good to get yourself an accountant, if only for some initial advice. Whatever structure you use, you'll need to draw up accounts for the business to support your tax return, and the apportionment of partnership profits between partners for tax purposes is often not straightforward. Both a partnership return
and individual income tax self-assessment returns will need to be submitted to HMRC.