North of Tromso in May

Tromso
http://www.yr.no/place/Norway/Troms/Tromsø/Tromsø/statistics.html
Svolvaer (Lofoten)
http://www.yr.no/place/Norway/Nordland/Vågan/Svolvær/statistics.html
Alta (Finnmark)
http://www.yr.no/sted/Norge/Finnmark/Alta/Alta/statistikk.html

In summary, a cold day will have max temp about 5C and a warm day about 12C. Frosts are infrequent. Precipitation is frequent but it is a relatively dry month, so on balance it shouldn't rain so much. It will mostly be in the form of rain but some snow or hail from time to time is possible. The snow cover on the land will mostly have gone by mid-May at lower altitudes.

petrol: same level as rest of Europe (not low tax even though Norway is the largest oilexporter in Europe) - some 13 NOK/L - but even with the big distaces in Scandinavia it is limited how many ful tanks you can use in that relatively limited area driving a European fuel efficient car.

Thanks for both responses. Great info!