Many years ago I borrowed slides for a presentation from a doctor of whom I have no recollection of. I was supposed to return them and I never did. there is no way for me to figure out who I borrowed them from. — I was wondering is there any way to do teshuva for this. Does giving money to some organization that dealt in his field of medicine or doing anything else help me to do teshuva?
You should use the monetary equivalent of the slides for some communal service (not to charity; see sources, below), where there is a possibility that the doctor or his inheritors will actually derive benefit from the service.
Concerning shepherds (whose animals were allowed to graze on private property) and tax collectors (who did not collect justly) the Shulchan Aruch (based on the Gemara) makes a suggestion of using the stolen money for communal needs (Choshen Mishpat 366:2). The same suggestion is made for a shopkeeper who made use of imprecise weights and measures (Choshen Mishpat 231:19).
What is defined as communal needs? With regard to somebody who stole money, but cannot recall who he stole from, the Gemara (Beitza 29a) recommends investing the money in public wells. Ahavas Chesed, quoting from the Shelah, adds that one may also use the money to buy sefarim for the local shul.
Today, the latter would be a more practical option that trying to pay for road repairs. It is important to note that the contribution should be made to as broad a communal need as possible. Giving the money to charity, whereby only the poor will benefit, is not an acceptable alternative (see Pischei Choshen, Geneivah Chap. 4, note 20). Upon donating the money or performing the service, one should beware of receiving undue honour on account of the contribution (Iggros Moshe, Choshen Mishpat 88).
We should note that the list of individuals who might be required to make some form of communal contribution is not short. It would certainly include shopkeepers who discover that weights and measures were not calibrated, gabbaim who made miscalculations or improper rounding-ups, government and municipality clerks who might have somehow slipped up, and any similar instance of involvement with the general public.
Apparently, the idea can also be applied to somebody who borrowed or damaged an item (such as a pen, a stamp, eggs, and so on) and cannot remember who the owner was.
It should be noted that although halachah advises the person in question to donate the money, or monetary equivalent, to a communal cause, this does not mend the transgression as completely as returning the money to the true owner (see Semah 231:34). If the doctor from whom the slides were borrowed can be identified, a full obligation remains (where applicable) to return them (or the monetary equivalent; see Meiri, Chibur Ha-Teshuvah 1:11).
Yet, the Aruch Ha-Shulchan explains that there is more to public service than simply doing good deeds with an ill-gotten gain. Because a person sincerely wishes to repent, Hashem assists him in his teshuvah, and arranges for the original victim, or one of the victim’s inheritors, to benefit from the service. In this way, the transgression is entirely rectified.
Best wishes, and sorry for lateness of reply — I believe the question was lost during a couple of days when the site was changing servers.