First of alla use 3,3v, you nerd alogic level convert.

Then you have to understand spi is not the main protocol used by SD, and that arduino should use SDSC to be sure, as some library was SDSC only.

Then you may have a HW problem: " SDHC cards have a 3.3 V bus so most Adruino shields, like the Wave Shield, use a resistor voltage divider to shift bus levels from 5V to 3.3V. These voltage dividers can not meet the 10 ns rise time for most SDHC cards. " from https://forums.adafruit.com/viewtopic.php?f=31&t=8738

Also using external power source MAY solve your trouble

First of all, use 3.3 V. You need a logic-level converter.

Then you have to understand SPI is not the main protocol used by SD cards, and that Arduino should use SDSC to be sure, as some libraries are SDSC only.

Then you may have a hardware problem (from FAT32/SDHC library for Wave and other shields):

SDHC cards have a 3.3 V bus so most Adruino shields, like the Wave Shield, use a resistor voltage divider to shift bus levels from 5 V to 3.3 V. These voltage dividers can not meet the 10 ns rise time for most SDHC cards."

Also using an external power source may solve your trouble.