Hello, best way to use AAS Flame or GFA or ICP-OS, ICP-MS after microwave digestion of your cell samples. Depends which sensitivity you need you can chose one of above mentioned technique.
It depends on what you mean by "best". Cheapest? Most accurate? Fastest turnaround time? Least amount of sample (given you are talking cell culture, you probably don't have litres of liquid to spare)? Least sample preparation by yourself?
Assuming you would like all 5 elements from the same sample, you are looking at ICP OES or ICPMS. Talk your preferred laboratory staff and explain 1) what elements you require in your analysis, 2) how much solution you can supply them and 3) how much money you have for the analysis (most labs require some sort of payment!).
Then ask them: what you need to supply them with (labelled samples, list of elements required, description of solution including any organic solvents, treatments to the samples etc). If you just send a bunch of unannounced, unlabelled samples with no description or explanation, you probably won't get the "best" results.
(You may note some experience in sample receivals from me in the above, but the only thing worse than unlabelled samples is the sender asking for results before I've even had a chance to talk to them about what I might be putting through my instrument).