Hi Jellyroll (I like that username!),

As Shutterbug mentioned, both cameras offer the Macro feature allowing you to get those fabulous close-up shots you wrote you'd like to take. The Fuji lets you focus as close as .3 inch and the Minolta lets you focus as close as 1.6 inches. Both are well suited for Macro mode close-up photography of such things as flower, insects, etc. Remember that you'll want to be very steady at this short distance so that your images won't be blurry. If you have a tripod, you'll want to use it.
As for telephoto capabilities, both have nice telephoto focal lengths comparable to 35mm equivalents of 370mm-Fuji and 380mm-Minolta. These lengths will be just dandy for photographing animals at moderate distances. I noticed that Fuji also offers an optional telephoto conversion lens which turns that 370mm into a 555mm. That's super for wildlife photography. Remember you'll want to maintain a safe distance from all wildlife both for your safety and theirs. (Please, if you would, read about wildlife photography ethics here at
http://www.digicamhelp.com/learn/other-articles/wildlife-photography.htm. Thanks!) I'm not sure if Minolta offers that lens option; it may. Oh yes, you'll want to use a tripod for those long focal lengths too. That's not a bad thing. I've become so used to carrying mine around that I feel naked without it.

Also, I've taken the liberty of including a couple of links to product reviews. Admittedly, I'm a nut for a indepth investigative review (chuckle). So, for a review of the Fuji S5000, go to
http://www.steves-digicams.com/2003_reviews/fuji_s5000_pg3.html. For a review of the Minolta Dimage Z1 you can go to
http://www.steves-digicams.com/2003_reviews/z1_pg3.html. These are just two, but you will find more if you do a search. Reading them may help with your decision making.
Hope this helps.
Holler if we can assist you further.
Cheers!