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You could try ethical saving? abundancegeneration.com give you the opportunity to invest in wind turbines or solar power with a 6-8% annual return. Its easy to do as the whole process is via their website. I'm thinking of doing it for my DS and DD.
You don't mention how old your daughter is, or what the eventual purpose of the money is. However, assuming you're looking for something over 5 years or more, want equity returns with a low level of involvement, then something like the following might be appropriate:
There are similar plans available from other providers (e.g. Witan 'jump').
Both of these invest in the stock market, but are relatively low cost. They've also been around for a while, and are low risk (where risk is defined as 'less volatile' - they may still drop below your initial investment).
If it's shorter term, then fixed-term savings bonds are likely to be the best option. NS&I offer childrens bonds (not really good value though, but utterly safe).
Savings accounts are generally crap, although Halifax has reasonable-ish rates. It all comes down to how long you want to invest for.
You should also consider the source of the cash - if it's you (i.e. the parent), then any interest over £100 in a year is taxable as though it was earned by the parent. If this is from grandparents/legacy/olympic paper round, then be sure to keep an audit trail.
For your £5,000, it depends what you want to do with it - might you need hasty access to it if your car breaks down? Are you happy to take a risk for higher returns?
Options are: - stick it in a savings account, - stick it in a fixed-term bond, - put it in a S&S ISA, and invest in corporate bonds/income fund - put it in a S&S ISA and invest in equities (FTSE index-tracker) - put it in a S&S ISA and invest in equities (peruvian tin-mining or something mad) - Zopa/Fundingcircle - Premium bonds / the 3.30 at Kempton park