design
Yes it is possible to do. Much depends on how accurately the output has to get to ground and to +5 volts and how linear is the triangle wave. The more tightly these are constrained the more circuitry and complexity there will be.
A moderate, simple solution with pretty good accuracy and linearity is outlined here. This is a concept, not a design. The basic oscillator is a
555 with a high enough frequency range. The threshold and trigger terminals (2 and 6) are tied together . An up current source pulls these terminals high and a down current source pulls these terminals low. The up current source is exactly twice the value of the down current source, say two millamps and one milliamp. A timing capacitor is connected from these terminals to ground. The discharge pin of the 555 (7) is connected to terminals two and six through diodes such that when the switch is on the current of the upper current source is diverted into pin 7. In this way the current available to charge and discharge the cap will be plus and minus one milliamp and a triangle wave will appear across the cap when the circuit is running.An op-amp with sufficient slew rate and bandwidth and who's output can swing near ground and +V is connected to the timing capacitor in a non-inverting connection. With appropriate gain and offset it will amplify the triangle wave and give an output that swings near ground and +V.
If more voltage is needed in the design than the available 5 volts, the square wave output of the 555 can be used with diodes and caps to boost the available power supply voltage to nearly 10 volts or even higher. This may make it easier to get the requisite gain and output swing for your gnd to +5 output requirement.
This is a simple scheme, easy to make work requiring no code or programming. You are basically making a function generator. Note that a square wave output is also available on pin 3 of the 555.