Call me crazy, but I swear I see a resemblence between the German word for 5: take fünf; morph the /f/s into /p/s as occasionally happens (cf. Welsh ceffyl vs. Irish capall, both cognates meaning "horse"); replace the /ü/ with /i/ (vowels foreign to one language are often merged with familiar values); and the /n/ becomes an /m/ because /np/ is always a tricky cluster and often gets slurred into /m/; (cf. the prefix in- becoming im- before words that start with m or p).
But all of the other numbers seem either Latinate (un, dau, tri, maybe naw) or unrelated to anything I'm familiar with (pedwar? chwech?).
Yes, pump and fünf are related. pump is also related to Latin quinque and thus also French cinq etc.
Welsh is P-Celtic, meaning that Proto-Indo-European "kw-" turned into "p-" (hence the many question words with p- where Latin has qu- and English has wh- and German w-). Irish is Q-Celtic, on the other hand, so it has c- (earlier q-, I believe) in such places.
So the word that gave Latin quinque and Greek pente (penkwe or something like that) gave something like quenque in early Celtic, then pempe and then pimpe in early Brythonic, then finally pump in modern Welsh. (pymp in Cornish. Always a source of titters for schoolboys. Along with poos for "heavy" or hwor for "sister".)
pedwar is just tetra/quattuor (as in quatro-) in disguise, from PIE kwetwor or so. And chwech is related to Latin sex, from PIE sweks or so.
Celtic is more closely related to Romance (and thus Latin) than to Germanic, so it's not surprising that some of the words still look similar - though some relationships are rather obscured by sound changes.