A multiple-entry visa for two years or more costs the same as a single-entry for a couple of weeks, so it's obviously worth it if you can get one. But if you don't have a genuine need to regularly visit the Schengen area, you are unlikely to get it.
As far as I know, there is little harm in applying for a multiple-entry visa (i.e. in checking the “multiple entry” box on the application form). There is nothing in the relevant regulation or published guidelines suggesting it would weigh against you and it's not one of the official reasons for refusal. It might make you look foolish but I doubt it could make or break an application (see also Does applying for a multiple entry Schengen visa instead of a single entry the first time hurt my chances of a visa getting granted?).
At the same time, multiple-entry visas are explicitly reserved for reliable applicants who have proved they respected the conditions of previous visas and need to visit the Schengen area frequently. For example, business or scientific research are among the reasons listed in the regulation. So “trying to get a multiple-entry visa” and having a credible need for regular travel is basically the same. If you can't find (and document!) something better than tourism, your odds are probably very bad and there isn't much else you can do.
It seems therefore unlikely you would get a multiple-entry visa in your situation. Having used a single-entry visa before should be in your favor but that's probably not enough and if the only purpose for your trip is tourism there is no reason for the consulate to issue a multiple-entry visa.
At the end of the day, consulates issue what they want (and sometimes make mistakes, too). You can't gamble and force them to choose between a multiple-entry visa and refusal; they can always issue a single or two-entry visa instead if they think it's appropriate. They do even sometimes issue multiple-entry visas even if they weren't asked for it (remember that one purpose of these visas is lowering the administrative burden for them, so if they think you are a low-risk traveller and you are likely to travel again in the near future they might as well spare themselves the need to process repeated applications).
Furthermore, I don't have any solid source for this, but I think five-year visas are mostly issued to UK residents and, possibly, to people with an extensive history of travel to the Schengen area. If you are lucky enough to get a multiple-entry visa this time around, it's likely to be a one-year visa and there is really nothing you can do about it beyond using this one correctly and hoping it helps you get a longer one next time.