5-ish hours a week may be hard to get and to make work, especially if you have no prior experience. Think about it – for tax season, there's about 10 weeks of busy season. If you worked all busy season, by the end of it, you'd have 50 hours in – less than a full busy season week. You'd still be having to ask them complete beginner questions at the end of the season. So, for them, it'd be a whole season of trying to train you without ever getting to benefit from having a trained assistant. I'd suggest trying to do some work with VITA or H&R Block this year to get your feet wet, then seeing if next year you could be a quasi-trained extra set of hands and be more useful to someone.
All that being said, you could be useful to the right person, especially if you could do more like 10-15 hours a week during busy season. I've worked in 2 super-small accounting firms (like, 1 full time owner/employee and a second almost-full-time or full-time employee), and both would've loved an extra set of hands during tax season, and maybe even year-round. At one of these firms, I was the 2nd full-time person, and we had a college kid working 10-15 hours a week. There were times that he was just copying paperwork, but there were times that the boss and I were just copying paperwork, too. That time of year, we all just did what had to be done to get it done. At the other firm, I was temporarily the 5-10 hours a week assistant for busy season. It became apparent after a few weeks, though, that the owner was expecting more hours than I could offer, so that ended up not working out. The 5-10 hours a week position, though, was after I'd worked the other one, so I came in as a trained employee. Actually, that guy was switching to the tax prep software that I'd used at my previous job, so I knew his software better than he did, so I was software consultant as well as tax employee. Anyway, as a trained person, I was useful to him…but if I didn't know my way around a tax return yet, I wouldn't have been useful.
So…I would say, helping out some is a great idea, but may have to wait till next year. If you could do a few hours year-round and more during tax season, then something year-round might work out, since the few hours a week would keep you all in touch and you familiar with the office, their methods, etc.; however, if a few hours a week is all you can do, it's likely that they wouldn't need you year-round.
Also, if you are still pretty young, you could try inquiring about part-time internships, as this would indicate your desire to learn and internships aren't always paid. Asking for an unpaid job looks more like you're desperate or up to something. Small CPA firms are often very protective of their client lists and may see someone asking if they can volunteer as someone trying to steal clients. It's sad that they see it this way, but I've worked with some who would.
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